Interest in spin-torque oscillators (STOs) has been increasing due to their potential use in communication devices. In particular the magnetic tunnel junction-based STO (MTJ-STO) with high perpendicular anisotropy is gaining attention since it can generate high output power. In this paper, a circuit-level model for an in-plane magnetized MTJ-STO with partial perpendicular anisotropy is proposed. The model includes the perpendicular torque and the shift field for more accurate modeling. The bias voltage dependence of perpendicular torque is represented as quadratic. The model is written in Verilog-A, and simulated using HSPICE simulator with a current-mirror circuit and a multi-stage wideband amplifier. The simulation results show the proposed model can accurately replicate the experimental data such that the power increases and the frequency decreases as the value of the perpendicular anisotropy gets close to the value of the demagnetizing field.