In phase II and/or III clinical trial study, there are several competing treatments, the goal is to assess the performances of the treatments at the end of the study, the trial design aims to minimize risks to the patients in the trial, according to some given allocation optimality criterion. Recently, a new type of clinical trial, the staggered-start trial has been proposed in some studies, in which different treatments enter the same trial at different times. Some basic questions for this trial are whether optimality can still be kept? under what conditions? and if so how to allocate the the coming patients to treatments to achieve such optimality? Here we propose and study a class of adaptive designs of staggered-start clinical trials, in which for given optimality criterion object, we show that as long as the initial sizes at the beginning of the successive trials are not too large relative to the total sample size, the proposed design can still achieve optimality criterion asymptotically for the allocation proportions as the ordinary trials; if these initial sample sizes have about the same magnitude as the total sample size, full optimality cannot be achieved. The proposed method is simple to use and is illustrated with several examples and a simulation study.