An adaptive sliding mode guidance law guiding the line-of-sight angular rate to converge to zero was highly appraised. However, compared with the conventional proportional navigation law, adaptive sliding mode guidance law leads to large acceleration demand of the interceptor before the line-of-sight angular rate converging to zero, especially in a situation where the target has strong manoeuvrability as well as high velocity. In this paper, a strategy making the coefficients of the guidance law vary according to a fuzzy rule is proposed. Smaller guidance coefficients are selected at the beginning of the terminal guidance. Therefore, the guidance command is reduced and a smaller acceleration of the interceptor is incurred. As the coefficients grow to the fixed and desired values, the line-of-sight angular rate converges to zero rapidly, so that the convergence to the sliding surface is guaranteed. It is concluded that the fuzzy variable coefficients strategy is highly effective for tail-chase, head-on interception and head pursuit engagements as shown in the simulations.