A hybrid powertrain has an engine, an input member, an output member, and a stationary member, and includes a single planetary gear set having a first, a second, and a third member. The input member is connected for common rotation with the engine and the output member is connected for common rotation with the second member. A single motor/generator is continuously connected for common rotation with the third member. A starter motor is operatively connected to the engine for starting the engine. A first torque-transmitting mechanism is selectively engagable to connect the input member for rotation with the first member. A second torque-transmitting mechanism is selectively engagable to ground the first member to the stationary member. A third torque-transmitting mechanism is selectively engagable to ground the third member to the stationary member. The powertrain is operable in an electric-only operating mode, an engine-only operating mode, and an electrically-variable operating mode.