Magnetic field-free switching of a three-terminal perpendicular magnetic tunnel junction driven by spin-orbit torque (SOT) and spin-transfer torque (STT) in the presence of a voltage-controlled magnetic anisotropy (VCMA) effect was investigated using micromagnetic simulation at 300 K. The VCMA effect assists or hinders magnetization switching depending on the polarity of the applied voltage. Thus, the impact of these effects on switching probabilities was evaluated using two write voltage pulses (V SOT, V STT). By optimizing the configuration of these voltage pulses, we demonstrated 100 successful switchings out of 100 trials within 3.2 ns under a limit voltage of 1.0 V. In addition, the write power consumption for SOT-STT writing with optimal pulse configurations was found to be one order of magnitude lower than that of STT-alone writing. We also found that the SOT-STT writing has the great potential in practical use compared with the external magnetic field assisted SOT-writing. Field-free, reliable, and deterministic SOT-STT switching with low power consumption offers significant advantages for embedded memory applications.