Conventionally, phase I dose-finding trials aim to determine the maximum tolerated dose of a new drug under the assumption that both toxicity and efficacy monotonically increase with the dose. This paradigm, however, is not suitable for some molecularly targeted agents, such as monoclonal antibodies, for which efficacy often increases initially with the dose and then plateaus. For molecularly targeted agents, the goal is to find the optimal dose, defined as the lowest safe dose that achieves the highest efficacy. We develop a Bayesian phase I/II dose-finding design to find the optimal dose. We employ a logistic model with a plateau parameter to capture the increasing-then-plateau feature of the dose–efficacy relationship. We take the weighted likelihood approach to accommodate for the case where efficacy is possibly late-onset. Based on observed data, we continuously update the posterior estimates of toxicity and efficacy probabilities and adaptively assign patients to the optimal dose. The simulation studies show that the proposed design has good operating characteristics. This method is going to be applied in more than two phase I clinical trials as no other method is available for this specific setting. We also provide an R package dfmta that can be downloaded from CRAN website.