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 stop control portion configured to control the first and second electric motors so as to generate torques in respective opposite directions when the engine is required to be stopped during running of the hybrid vehicle in an engine drive mode in which the clutch is placed in an engaged state, the engine stop control portion reversing the directions of the torques generated by the first and second electric motors while the hybrid vehicle is in a coasting run, with respect to those generated while the hybrid vehicle is in a positive driving run.