The crystallization of monodisperse linear polyethylene confined in nanoporous alumina is investigated with the calorimetric measurements. We observe a drastic change in crystallization behavior, specifically nucleation, with a decrease in the pore diameter. Crystallization in relatively larger pores with the diameters of 62 and 110 nm occurs at lower temperatures within a very narrow range, whereas crystallization in smaller pores with diameters of 15-48 nm occurs at a higher and broad range of temperatures. Nucleation and crystallization kinetics in nanopores is discussed based on classical nucleation theory as well as the Avrami theory.