The goal of a dose-finding trial for the latest anti-cancer agents, e.g., molecular targeted, cytostatic, and biological agents, as well as immune-oncology therapy, is to identify the optimal dose (OD), defined as the tolerable dose having adequate efficacy under the unpredictable dose–toxicity and dose–efficacy relationships. Although several approaches have been suggested for identifying ODs by incorporating both efficacy and toxicity responses in dose-finding trials, these approaches ignore the late-onset outcome and the outcome evaluation period. When the outcome is of late-onset and the evaluation periods are different between efficacy and toxicity outcomes, some enrolled patients may not have completed their outcome assessments by the interim decision making. To solve these issues, we propose a time-to-event Bayesian optimal interval design based on both efficacy and toxicity outcomes (TITE-BOIN-ET design) to accelerate identifying an OD using the cumulative and pending data. A simulation study shows the TITE-BOIN-ET design has advantages than the other approaches across a variety of realistic settings.