We report the recent progress of our pulsed optically pumped (POP) vapor cell rubidium clock with dispersive detection. A new compact physics package is made. A rubidium cell with a high precision buffer gases mixing ratio is obtained, and the temperature controlling system is renovated to reduce fractional frequency sensitivity to temperature variation. The resolution of the servo control voltage is also optimized. With these improvements, a clock frequency stability of $3.53\times {10}^{13}$ at 1 s is obtained, and a fractional frequency stability of $4.91\times {10}^{15}$ is achieved at an average time of $\tau =2000\mathrm{s}$.