In this paper, we propose a meshless method for option pricing which uses the radial basis quasi-interpolation method to solve the Black-Scholes equation. The quasi-interpolation operator is used to force the first and second derivatives of stock prices in spatial direction and the forward difference method is used in time direction. Its convergence of order $o (Δt+ h^{\frac{2}{3}})$ in $l_∞$−norm is also derived in the paper. The advantage of this method is that it can fit the scattered data well, which makes it be a good approximation method for the option prices that fluctuate randomly. The feasibility of the proposed method is verified by numerical examples of uniform points and scattered points. The results show that this method has a good fitting effect on option prices.