A method for starting an engine of a vehicle having a hybrid transmission is provided. The hybrid transmission is capable of providing motor running under a power of an electric motor only and hybrid running under a power of both of the engine and the electric motor. The power of an engine is supplied to the hybrid transmission by way of a clutch. The method includes, when the clutch is engaged for starting the engine during the motor running, issuing an engine start instruction when an engine speed increases to a startable speed with the progress of engagement of the clutch, and after the moment of issue of the engine start instruction, restricting increase of an engagement force of the clutch and thereby suppressing the progress of engagement of the clutch. An apparatus for carrying out the method is also provided.