Record list : highest score by a batsman in IPL T20 matches.
Chris Gayle has made the highest score in IPL. If there is an almost as much tougher twenty20 stage than international matches, its IPL and hence, if there is a list that's second most pretigious to have a name in to highest T20 score, is highest individual score in IPL, of which we have a list in following..

Chris Gayle, the big Jamaican, has easily been the most dangerous batsman in IPL and he proved it to Pune Warriors on 23rd April 2013, smashing the highest score in T20 cricket anywhere in the world as well as the fastest century in the tournament, off just 30 balls! Gayle hit 17 sixes, the most by any batsman in an inning.

Brendon McCullum, the New Zealand swashbuckler, in the very first match in the history of Indian Premier League, struck a mind boggling 158 without being dismissed which stood as best score for more than five seasons. The game was played at M Chinnaswamy stadium in Bangalore and against the home team Royal Challengers, this Kolkata Knight Riders right handed opener mesmerized everyone, reaching fifty off 32 balls (5 fours + 3 sixes), hundred off 53 balls (8 fours + 7 sixes) and then 150 off 70 balls (10 fours and 12 sixes). Needless to say, McCullum concentrated on hitting everything out of the park once he got set and succeeded admirably.

Fact : only 30 batsmen have been able to score a century in IPL matches and hence, they're the only ones featuring in following list. Chris Gayle is the batsman to score most centuries in IPL = 4, followed by Virender Sehwag, Murali Vijay, David Warner, Adam Gilchrist and Brendon McCullum who all have two. 16 others have one ton each.

Related : Fastest century in IPL | Fastest fifties.
Highest individual scores by a batsman in IPL T20 matches.
Batsman (Team) Score Balls 4s 6s Versus Date
Chris Gayle (Bangalore) 175* 66 13 17 Pune 23 Apr 2013
Brendon McCullum (Kolkata) 158* 73 10 13 Bangalore 18 Apr 2008
Chris Gayle (Bangalore) 128* 62 7 13 Delhi 17 May 2012
Murali Vijay (Chennai) 127 56 8 11 Rajasthan 3 Apr 2010
Virender Sehwag (Punjab) 122 58 12 8 Chennai 30 May 2014
Paul Valthaty (Punjab) 120* 63 19 2 Chennai 13 Apr 2011
Virendra Sehwag (Delhi) 119 56 13 6 Deccan 5 May 2011
Andrew Symonds (Deccan) 117* 53 11 7 Rajasthan 24 Apr 2008
Michael Hussey (Chennai) 116* 54 8 9 Punjab 19 Apr 2008
Wridhiman Saha (Punjab) 115* 55 12 8 Kolkata 1 Jun 2014
Shaun Marsh (Punjab) 115 69 11 7 Rajasthan 28 May 2008
Sanath Jayasuriya (Mumbai) 114* 48 9 11 Chennai 14 May 2008
Manish Pandey (Bangalore) 114* 73 10 4 Deccan 21 May 2009
Murali Vijay (Chennai) 113 58 15 4 Delhi 25 May 2012
Mahela Jayawardene (Punjab) 110* 59 14 3 Kolkata 4 Apr 2010
David Warner (Delhi) 109* 54 10 7 Deccan 10 May 2012
Rohit Sharma (Mumbai) 109* 60 12 5 Kolkata 12 May 2012
Adam Gilchrist (Deccan) 109* 47 9 10 Mumbai 27 Apr 2008
David Warner (Delhi) 107* 69 9 5 Kolkata 29 Mar 2010
Chris Gayle (Bangalore) 107 49 10 9 Deccan 6 May 2011
Adam Gilchrist (Punjab) 106 55 8 9 Bangalore 17 May 2011
AB de Villiers (Delhi) 105* 54 5 6 Chennai 23 Apr 2009
Kevin Pietersen (Delhi) 103* 64 6 9 Deccan 19 Apr 2012
Ajinkya Rahane (Rajasthan) 103* 60 12 5 Bangalore 15 Apr 2012
Chris Gayle (Bangalore) 102* 55 10 7 Kolkata 22 Apr 2011
David Miller (Punjab) 101* 38 8 7 Bangalore 6 May 2013
Shane Watson (Rajasthan) 101 61 6 6 Chennai 22 Apr 2013
Suresh Raina (Chennai) 100* 53 7 6 Punjab 2 May 2013
Brendon McCullum (Chennai) 100* 56 8 9 Hyderabad 11 Apr 2015
Lendl Simmons (Mumbai) 100* 61 14 2 Punjab 21 May 2014
Sachin Tendulkar (Mumbai) 100* 66 12 3 Kochi 15 Apr 2011
Yusuf Pathan (Rajasthan) 100 37 9 8 Mumbai 13 Mar 2010
Suresh Raina (Chennai) 99* 52 11 3 Hyderabad 8 May 2013
Virat Kohli (Bangalore) 99 58 10 4 Delhi 10 May 2013