Conventional methods for mediation analysis generate biased results when the mediator-outcome relationship depends on the treatment condition. This article introduces a new technique, ratio-of-mediator-probability weighting (RMPW), for decomposing total effects into direct and indirect effects in the presence of treatment-by-mediator interactions. The indirect effect can be further decomposed into a pure indirect effect and a natural treatment-by-mediator interaction effect. The latter captures the treatment effect transmitted through a change in the mediational process. We illustrate how to apply the technique to identifying whether employment mediated the relationship between an experimental welfare program and maternal depression. In comparison with other techniques for mediation analysis, RMPW requires relatively few assumptions about the distribution of the outcome, the distribution of the mediator, and the functional form of the outcome model, and is easy to implement using standard statistical software. Simulation results reveal satisfactory performance of the parametric and non-parametric RMPW procedures under the identification assumptions and show a relatively higher level of robustness of the non-parametric procedure. We provide a tutorial and Stata code for implementing this technique.