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Spin-torque induced magnetization dynamics in a spin-torque oscillator with an in-plane (IP) magnetized free layer and an out-of-plane (OP) magnetized polarizer under IP shape-anisotropy field (Hk) and applied IP magnetic field (Ha) was theoretically studied based on the macrospin model. The rigorous analytical expression of the critical current density (Jc1) for the OP precession was obtained. The obtained expression successfully reproduces the experimentally obtained Ha-dependence of Jc1 reported in [D. Houssameddine et al., Nat. Mater. 6, 447 (2007)].