A greedy nonintrusive reduced order method (ROM) is proposed for parameterized time-dependent problems with an emphasis on problems in fluid dynamics. The nonintrusive ROM (NIROM) bases on a two-level proper orthogonal decomposition to extract temporal and spatial reduced basis from a set of candidates, and adopts the radial basis function to approximate undetermined coefficients of extracted reduced basis. Instead of adopting uniform or random sampling strategies, the candidates are determined by an adaptive greedy approach to minimize the overall offline computational cost. Numerical studies are presented for a two-dimensional diffusion problem as well as a lid-driven cavity problem governed by incompressible Navier–Stokes equations. The results demonstrate that the greedy nonintrusive ROM (GNIROM) predicts the flow field accurately and efficiently.