A gas turbine combustor comprising: a combustion chamber inside which a combustion space is formed; and an acoustic liner that is provided outside the combustion chamber and defines an acoustic space between the acoustic liner and an outer peripheral surface of the combustion chamber, wherein through-holes (16,16a;36a;46a) through which the combustion space communicates with the acoustic space are formed in a wall of the combustion chamber, a plurality of rows of the through-holes (16,16a;36a;46a) in which each row includes some of the through-holes (16,16a;36a;46a) aligned in a circumferential direction of the combustion chamber is arranged in a lengthwise direction of the combustion chamber, the through-holes (16,16a;36a;46a) of a first through-hole row are shifted with respect to the through-holes (16,16a;36a;46a) of a second through-hole row adjacent to the first through-hole row so that centers of the through-holes (16,16a;36a;46a) of the first and second through-hole rows adjacent each other are staggered in the circumferential direction, the through-holes (16,16a;36a;46a) of the first through-hole row and the through-holes (16,16a) of the second through-hole row overlap in the circumferential direction, cooling grooves (17;27) are formed so as to avoid the through-holes (16,16a;36a;46a) on the inside that is sandwiched between the outer peripheral surface and the inner peripheral surface of the combustion chamber and corresponds to a position where the acoustic liner is provided, and characterized in that the cooling grooves (17;27) include transverse cooling grooves extending in the circumferential direction between rows of the through-holes (16,16a;36a;46a), and longitudinal cooling grooves extending in the lengthwise direction between the through-holes (16,16a;36a;46a) and connecting the transverse cooling grooves adjacent to each other in the lengthwise direction. a combustion chamber inside which a combustion space is formed; and an acoustic liner that is provided outside the combustion chamber and defines an acoustic space between the acoustic liner and an outer peripheral surface of the combustion chamber, wherein through-holes (16,16a;36a;46a) through which the combustion space communicates with the acoustic space are formed in a wall of the combustion chamber, a plurality of rows of the through-holes (16,16a;36a;46a) in which each row includes some of the through-holes (16,16a;36a;46a) aligned in a circumferential direction of the combustion chamber is arranged in a lengthwise direction of the combustion chamber, the through-holes (16,16a;36a;46a) of a first through-hole row are shifted with respect to the through-holes (16,16a;36a;46a) of a second through-hole row adjacent to the first through-hole row so that centers of the through-holes (16,16a;36a;46a) of the first and second through-hole rows adjacent each other are staggered in the circumferential direction, the through-holes (16,16a;36a;46a) of the first through-hole row and the through-holes (16,16a) of the second through-hole row overlap in the circumferential direction, cooling grooves (17;27) are formed so as to avoid the through-holes (16,16a;36a;46a) on the inside that is sandwiched between the outer peripheral surface and the inner peripheral surface of the combustion chamber and corresponds to a position where the acoustic liner is provided, and characterized in that the cooling grooves (17;27) include transverse cooling grooves extending in the circumferential direction between rows of the through-holes (16,16a;36a;46a), and longitudinal cooling grooves extending in the lengthwise direction between the through-holes (16,16a;36a;46a) and connecting the transverse cooling grooves adjacent to each other in the lengthwise direction.