Grade information has been considered in Yuan et al. (2007) wherein they proposed a Quasi-CRM method to incorporate the grade toxicity information in phase I trials. A potential problem with the Quasi-CRM model is that the choice of skeleton may dramatically vary the performance of the CRM model, which results in similar consequences for the Quasi-CRM model. In this paper, we propose a new model by utilizing bayesian model selection approach--Robust Quasi-CRM model--to tackle the above-mentioned pitfall with the Quasi-CRM model. The Robust Quasi-CRM model literally inherits the BMA-CRM model proposed by Yin and Yuan (2009) to consider a parallel of skeletons for Quasi-CRM. The superior performance of Robust Quasi-CRM model was demonstrated by extensive simulation studies. We conclude that the proposed method can be freely used in real practice.