We theoretically examine metastability occurring in magnetization relaxation for magnetic nanoparticles with size distributions. An array ofmagnetic nanoparticles is simulated using a spin S = 1 ferromagnetic Blume-Capel model on a square lattice. The particle size distributions give rise to distributions of magnetic anisotropy. Including the distributions, we perform kinetic Monte Carlo simulations of magnetization relaxation at low temperatures for the Blume-Capel model. We compute the average lifetime of the metastable state from the simulations and the absorbing Markov chains method in the low-temperature limit. We also carry out similar simulations and calculations for a constant value of magnetic anisotropy for comparison. Our results suggest that the lifetime of the metastable state is determined by the smallest particle for a given system, and that the lifetime with size distributions obeys a modified Arrhenius-like law, where the energy barrier depends on even temperature and standard deviation of the distributions as well as magnetic field and magnetic anisotropy.