Objective:We establish a projecting transformation from nonautonomous equation into autonomous one, and seek out explicit one-component and two-component solutions of a (2+1)-dimensional coupled nonautonomous nonlinear Schrödinger model for a partially nonlocal nonlinearity with a parabolic potential. Methods:We combine these solutions of autonomous one into the projecting transformation and use the Darboux method to find solutions. Result:We take into account a (2+1)-dimensional coupled nonautonomous nonlinear Schrödinger model for a partially nonlocal nonlinearity with a parabolic potential, and establish a projecting transformation from nonautonomous equation into autonomous one. Moreover, we seek out explicit one-component and two-component solutions, e.g. explicit Peregrine bump solution and explicit integrated breather solutions.