Abstract: In order to test the ability of FPM modelling natural convection problems, FPM was used to simulate natural convection in a closed square cavity. Firstly,FPM was depicted in detail, the Lagrangian N-S equations was discretized with FPM, and natural convection in a closed square was simulated at Ra=10⁴,10⁵,10⁶ based on the discretized equations. And then, velocity and temperature contours, non-dimensional velocity and temperature profiles along the centerline at different Rayleigh numbers were presented. The results show that FPM can obtain temperature field accurately at all three Rayleigh numbers and obtain velocity field accurately at low Raleigh numbers, but with increasing Raleigh numbers, the precision and stability of the velocity field is decreasing, so FPM still needs to be improved for getting more accurate and stable velocity fields.