A dual-output filter-free microwave photonic single sideband (SSB) up-converter with the mixing spurs highly suppressed is proposed and experimentally demonstrated. By introducing the balanced Hartley structure using a 90° optical hybrid, the lower sideband (LSB) and upper sideband (USB) up-converted RF signals can be generated simultaneously and output separately, with no need of either optical or electrical filtering. The structure avoids the special requirement with the optical modulation format of the local oscillator (LO) signal. The intermediate frequency signal is modulated with the optical carrier suppressed -SSB modulation format. The undesired optical components are highly suppressed. In this way, the high sideband and LO leakage suppression ratios of the SSB up-converter are guaranteed. The dual-output SSB up-conversion is experimentally achieved within the working frequency range of 10-30 GHz. The undesired sideband and LO leakage suppression ratios are larger than 67 dB for the whole frequency range. The spurious-free dynamic range of larger than 95.6dBc⋅Hz2/3 has also been achieved experimentally for both the LSB and USB up-conversion conditions.