The analytical solutions and numerical ones of parabolic equations in one space variable and the time variable are constructed by weak N-best pre-orthogonal adaptive Fourier decomposition method (weak N-best POAFD) in reproducing kernel Hilbert space (RKHS). To apply weak N-best POAFD, we first choose a dictionary for weak N-best POAFD and implement pre-orthonormalization to all dictionary elements. Then select some parameters by weak N-best maximal selection principle and determine some normalized dictionary elements iteratively. Thus, the analytical solution can be expressed as a linear combination of these determined normalized dictionary elements with a fast convergence rate. Some numerical examples confirm the good accuracy and applicability of the weak N-best POAFD method in solving the partial differential equations.