Abstract: For phase Ⅰ cancer clinical trials, toxicity is a major concern. Commonly, toxicity is categorized with five levels of severity. A simple sequential design that addresses these ethical concerns is the up-and-down designs (BCD Ⅰ, BCD Ⅱ, k-in-a-row, Narayana, improved Narayana). However, in the up-and-down designs family, the severity level of graded toxicity of a previous patient's response would not be a differentiated factor for "the next dose level assignment and doses that are too toxic may also be recommended. In this study, we extend the up-and-down procedure incorporating the idea on the assessments of graded toxicity in the dose escalation. We investigate the operating characteristics of this approach under a variety of dose-toxicity associations and comparison with up-and-down family shows that it can achieve significant improvements to the doses recommended during the phase Ⅰtrial.