Based on the spin-flip model, the nonlinear dynamics of a 1550 nm vertical-cavity surface-emitting laser (1550 nm-VCSEL) subject to dual-beam optically injection is investigated theoretically. The results show that a slave 1550 nm-VCSEL (S-VCSEL) under the injection of dual-beam output from two master VCSELs (M-VCSELs) can be driven to enter into an injection locking state under suitable injection parameters. In this case, the outputs of both X and Y polarization modes of the S-VCSEL exhibit periodic oscillation whose frequency is equal to the frequency detuning between the two M-VCSELs, and its optical spectrum contains only two main frequency components and possesses a single sideband spectrum structure. As a result, two mutually orthogonal optical millimeter-waves can be obtained based on the periodic oscillation in a VCSEL subject to dual-beam optically injected locking. Through adjusting the frequency detuning between the two M-VCSELs, the frequency of the millimeter-wave can be tuned continuously in a large range, while the power and modulation depth can also be controlled by adjusting the system parameters.