To reduce Touschek scattering in the beam and extend the lifetime of the beam in the Shenzhen Innovation Light-source Facility (a fourth-generation light source), a 1500 MHz passive third harmonic system will be used. The present work is devoted to the RF design and frequency sensitivity analysis of the 1500 MHz passive third harmonic superconducting cavity, optimizing the RF parameters of the cavity, and giving a frequency scheme for the cavity in fabrication. The reliability of the cavity during operation is taken as the main goal for the optimization of the geometrical parameters, and its structural and RF parameters are obtained with E peak/E acc of 2.17, B peak/E acc of 5.12 mT/(MV/m) and G · R/Q of 25052 at 2 K. A pair of fluted beam pipes are used to propagate the higher order modes (HOMs) of the harmonic cavity, allowing a smooth transition of the first dipole mode to the absorber located at room temperature area. For the frequency sensitivity analysis, the frequency variations of the cavity in fabrication are obtained by multi-physics coupling simulation in the paper, which gives the target frequency of the cavity between welding and preloading. After electron beam welding (EBW), the resonant frequency of the cavity should be maintained at 1500.096 MHz, and the pre-tuning target frequency is 1497.456 MHz. The slow tuning range is ±400 kHz, the fast-tuning range is 600 Hz, and the maximum allowable tuning force is 15 kN.