Based on an optically injected semiconductor laser (OISL) operating at period-one (P1) nonlinear dynamical state, high-purity millimeter-wave generation at 60 GHz band is experimentally demonstrated via 1/4 and 1/9 subharmonic microwave modulation (the order of subharmonic is with respect to the frequency fc of the acquired 60 GHz band millimeter-wave but not the fundamental frequency f0 of P1 oscillation). Optical injection is firstly used to drive a semiconductor laser into P1 state. For the OISL operates at P1 state with a fundamental frequency f0 = 49.43 GHz, by introducing 1/4 subharmonic modulation with a modulation frequency of fm = 15.32 GHz, a 60 GHz band millimeter-wave with central frequency fc = 61.28 GHz ( = 4fm) is experimentally generated, whose linewidth is below 1.6 kHz and SSB phase noise at offset frequency 10 kHz is about -96 dBc/Hz. For fm is varied between 13.58 GHz and 16.49 GHz, fc can be tuned from 54.32 GHz to 65.96 GHz under matched modulation power Pm. Moreover, for the OISL operates at P1 state with f0 = 45.02 GHz, a higher order subharmonic modulation (1/9) is introduced into the OISL for obtaining high-purity 60 GHz band microwave signal. With (fm, Pm) = (7.23 GHz, 13.00 dBm), a microwave signal at 65.07 GHz ( = 9fm) with a linewidth below 1.6 kHz and a SSB phase noise less than -98 dBc/Hz is experimentally generated. Also, the central frequency fc can be tuned in a certain range through adjusting fm and selecting matched Pm.