An algorithm based on eigenfunctions was proposed for phase retrieval by solving transport-of-intensity equation. The phase could be expanded as a series of Laplacian′s eigenfunctions, and the coefficients of eigenfunction could be obtained by the integral of eigenfunction and intensity derivative along the optical axis, then the phase was reconstructed. The analytic expressions of Laplacian′s eigenfunctions on unit circle and rectangular domain were achieved. Phase retrieval by eigenfunctions on both domains was simulated, and an accurate reconstruction result could be obtained by the algorithm.