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In this paper an explicit/implicit schemes for parabolic equations with discontinuous coefficients is analyzed. We show that the error of the solution in L∞ norm and the error of the discrete flux in L2 norm are in order O(τ + h2) and O(τ + h3/2), respectively and the scheme is stable under some weaker conditions, while the difference scheme has the truncation error O(1) at the neighboring points of the discontinuity of the coefficient. Numerical experiments, which are given for both linear and nonlinear problems, show that our theoretical estimates are optimal in some sense. The comparison with some classical scheme is presented. © 2004 Institute for Scientific Computing and Information.