Accompanying the sketch is a photograph of a Honda Dream motorbike, the type they believe was used in the botched handbag snatch and stabbing of Mrs Smith.
The sketch is accompanied by notes that describe the man they want, putting his age at 25 to 30, and his height at 175 to 180 cm.
In red text it also stresses the B300,000 reward offered for information leadingto his capture.
The sketch will be widely circulated around the island.
Anyone with information can call any police station or call Phuket Police Commander Maj Gen Chonasit Wattanavrangkul at 081 844 9559.