Spintronic devices offer low power consumption, built-in memory, high scalability and reconfigurability, and could therefore provide an alternative to traditional semiconductor-based electronic devices. However, for spintronic devices to be useful in computing, complementary logic operation using spintronic logic gates is likely to be required. Here we report a complementary spin logic device using electric-field controlled spin-orbit torque switching in a heavy metal/ferromagnet/oxide structure. We show that the critical current for spin-orbit-torque-induced switching of perpendicular magnetization can be efficiently modulated by an electric field via the voltage-controlled magnetic anisotropy effect. Moreover, the polarity of the voltage-controlled magnetic anisotropy can be tuned through modification of the oxidation state at the ferromagnet/oxide interface. This allows us to create both n-type and p-type spin logic devices and demonstrate complementary logic operation.