To solve the limitations of existing virtual oscillator control (VOC), this paper presents the Poincaré-type VOC (PVOC) for grid-forming inverters and further provides a passivity-based transient stability enhancement method for PVOC. First, the core equation of PVOC is formulated based on the Poincaré bifurcation equation, and its advantages of steady droop characteristics and dynamic performances are analyzed. Second, a passivity-based control for PVOC (PBC-PVOC) is designed based on the energy damping and pumping method to enhance the system transient stability. The method of passivating the closed-loop system is illustrated, and the passivity conditions and parameter selections are analyzed in detail. Subsequently, a virtual impedance based current limiting method is presented for PBC-PVOC to effectively prevent the overcurrent under large disturbances. Finally, the time-domain simulation and experiments are carried out for the effectiveness validation under multiple operating conditions.