A drive control device for a hybrid vehicle is provided with a differential device including four rotary elements; and an engine, first and second electric motors and an output rotary member which are respectively connected to the four rotary elements. One of the four rotary elements is constituted by a rotary component of a first differential mechanism and a rotary component of a second differential mechanism selectively connected through a clutch, and one of the rotary components is selectively fixed to a stationary member through a brake. The drive control device comprises: an engine start control portion configured to switch an operating state of the clutch during cranking of the engine to raise its speed for starting the engine. The engine start control portion includes: a first clutch controlling portion configured to place the clutch in one of a released state and an engaged state in which a difference between a first dwelling speed to be established in a first half period of a rise of a speed of the engine and a first resonance speed of a drive line extending from the engine to the first electric motor connected to the first differential mechanism through a torsional damper is larger in the other of the released and engaged states, the first resonance speed corresponding to an explosion 1-order frequency of the engine; and a second clutch controlling portion configured to place the clutch in one of the released and engaged states in which a difference between a second dwelling speed to be established in a second half period of the rise of the speed of the engine and a predetermined second resonance speed of the drive line is larger in the other of the released and engaged states, the predetermined second resonance speed corresponding to a revolution 0.5-order pulsation frequency of the engine.