Delayed treatment effects have been commonly observed in clinical trials, which bring more challenges to the interim decision making particularly in adaptive designs setting. An improper interim analysis may falsely stop a promising study based on the traditional conditional power (CP) approach. For such scenario, a short-term surrogate endpoint which is predictive of the primary long-term outcome can be extremely useful for a more accurate CP calculation and adaptative decision. In this paper, we propose utilizing a surrogate endpoint in the interim analysis to improve the CP calculation in designing an adaptive sample size re-estimation (SSR) study. Through theoretic derivation and extensive simulations, we show that our proposed approach demonstrates the practical feasibility and benefits of using a surrogate endpoint for adaptive designs with delayed treatment effects. We also demonstrate proposed approach in case studies of phase III Non-small cell lung cancer (NSCLC) trial with delayed treatment effect as well as Norovirus (NoV) vaccine trial. Finally, we give recommendations on how this method could be implemented in confirmatory clinical trials.