This paper presents an approximate analytical solution to one-dimensional model of the charging process for stratified thermal storage tanks, in which variation of the inlet temperature as well as the momemtum-induced mixing is taken into accout. The mixing is incorporated into the model as a constant-depth perfectly mixed layer above the plug flow region. Based on the superposition principle, the variable inlet temperature is approximated by a number of step functions. Temperature distributions for the thermocline corresponding to three types of interfacial condition arr successfully derived in terms of well-defined functions, so that a linear combination of them constitutes the final solution. Validity and utility of this work is examined through the comparison of the approximate solution with an exact solution available for the case of linearly increasing inlet temperature. With increasing the number of steps, the present solution asymptotically approaches to the exact one. Even with a limited number of steps, the present results favorably agree with those by the exact solution for a wide range of the mixing depth. Also, it is revealed that fewer steps are needed for meaningful predictions as the mixing. depth becomes larger.