In this paper, a fast numerical scheme for computing the European call options pricing problems governed by the Black Scholes equation was developed. Error analysis algorithm was developed from the proposed scheme. It is proved that the proposed scheme has second order accuracy in both time and space under some restrictions, the stability of the scheme in the sense of Non –Neumann analysis is presented. It is shown that the proposed scheme has a good performance in the sense of Errors, the computational cost and storage capacities compare to the Crank- Nicolson. Also the accuracy of the purposed scheme is better than the Semi- implicit scheme in most cases. Numerical examples are conducted to test the validity, efficiency, and accuracy of the proposed scheme.
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