A Global 5000 corporate jet, registered M-YSAI, while landing at runway 21 of Seletar Airport, experienced a strong gust of cross wind causing it to drift off and touch down on the left side of the runway. Both nose and left main gears touched down on the grass patch while the right main gear touched down on the edge of the paved runway. After touching down, the Pilot Flying manoeuvred the aircraft back onto the runway and subsequently taxied the aircraft to its parking bay. As a result of the runway excursion, two signboards on the left of the runway were damaged due to contact by the aircraft. The aircraft sustained damages to its left flaps, left flap track fairings, left landing gear door and left thrust reverser lower clamshell door. There was no injury to any person. CONCLUSION 1. The air traffic controller had informed the flight crew of a low level windshear warning indicating the presence of windshear activity in the aerodrome. As the aircraft approached the runway, the weather conditions deteriorated and this was detected by the aircraft’s windshear detection system. 2. The windshear caution was generated by the aircraft’s windshear detection system but the visual indication was not noticed by both pilots. When the windshear warning was generated later, the PF did not notice the visual and aural indications related to this warning and the PM noticed only the aural indication. 3. Although the PM heard the aural warning, he did not initiate a go-around, which was required by the Airplane Flight Manual.