We propose a new scheme to generate single-sideband (SSB) photonic vector millimeter-wave (mm-wave) signal adopting asymmetrical SSB modulation enabled by a single in-phase/quadrature (I/Q) modulator. The driving signal for the I/Q modulator is generated by software-based digital signal processing (DSP) instead of a complicated transmitter electrical circuit, which significantly simplifies the system architecture and increases system stability. One vector-modulated optical sideband and one unmodulated optical sideband, with different sideband frequencies, located at two sides of a significantly suppressed central optical carrier, are generated by the I/Q modulator and used for heterodyne beating to generate the electrical vector mm-wave signal. The two optical sidebands are robust to fiber dispersion and can be transmitted over relatively long-haul fiber. We experimentally demonstrate the generation and transmission of 4-Gbaud 80-GHz quadrature-phase-shift-keying-modulated (QPSK-modulated) SSB vector mm-wave signal over 240-km single-mode fiber-28 without optical dispersion compensation.