A Lagrangian-Eulerian (LE) approach is applied to solving reactive chemical transport problems of multi-component systems. The problem of negative concentrations is overcome with the LE approach. Two techniques of treating the Lagrangian step are included: one is to use the retarded velocity and the other is to adopt the pore velocity. The advantages and disadvantages of both techniques are compared and discussed. An attendant advantage of using the LE approach is that the resulting matrix equation is positive definite; thus one can use iteration methods, for example, the conjugate gradient method, to solve the matrix equation with convergency guaranteed.