In this paper, the modified equal width wave (MEW) equation is solved numerically using the cubic and septic B-spline. The proposed algorithms are based on Crank-Nicolson formulation and finite difference approximation. The non-linear term for cubic B-spline is computed during executing the algorithm at each time level in terms of the previous level while for septic B-spline we tackle the nonlinear term in the equation using a variant of the linearization technique. The stability analysis using Von-Neumann concept shows the schemes are unconditionally stable. To test accuracy the error norms $L_2$ and $L_\infty$ are computed.