A gas turbine combustor and a gas turbine; wherein inclined surfaces are provided on inner surfaces of side walls neighboring in a circumferential direction at downstream end portions of transition pieces of combustors, the inclined surfaces being configured to increase a passage area of the transition pieces, a ratio (S/P) is from 0 to 0.2, where (P) is a pitch dimension of first stage vanes, and (S) is a circumferential dimension from an intermediate point between neighboring transition pieces to an upstream end of a first stage vane closest in the circumferential direction; and a ratio (L/P) is from 0.3 to 0.55, where (P) is the pitch dimension, and (L) is an axial dimension from a downstream end of the transition piece to the upstream end of the first stage vane.