We calculate the inclusive production of h(c) (h(b)) at e(+)e(-) colliders with the center-of-mass energy from the CLEO-c energy to Z(0) boson mass at leading order of nonrelativistic QCD. At Z(0) boson mass, the cross sections are 39 similar to 703 fb for h(c) (1P), 37 similar to 61 fb for h(b) (1P), and 44 similar to 73 fb for h(b) (2P). At the B-factories, it is 86 similar to 212 fb for h(c) (1P). For h(c) at the CLEO-c and h(b) (1P, 2P) at the B-factories, the perturbative QCD expansion is not good and the results are much smaller than the experimental measurements. It is clearly shown in all the results that the color-octet state (S-1(0)8) contributes dominantly while the color-singlet state (P-1(1)1) contributes a small or even negative part, in contrast to the case of inclusive J/psi production where the color-singlet state is found to contribute dominantly.