We consider the case of phase I trials for treatment of cancer or other severe diseases in which grade information is available about the severity of toxicity. Most dose allocation procedures dichotomize toxicity grades based on being dose limiting, which may not work well for severe and possibly irreversible toxicities such as renal, liver, and neurological toxicities, or toxicities with long duration. We propose a simple extension to the continual reassessment method (CRM), called the Quasi-CRM, to incorporate grade information. Toxicity grades are first converted to numeric scores that reflect their impacts on the dose allocation procedure, and then incorporated into the CRM using the quasi-Bernoulli likelihood. A simulation study demonstrates that the Quasi-CRM is superior to the standard CRM and comparable to a univariate version of the Bekele and Thall method (2004, Journal of the American Statistical Association 99, 26-35). We also present sensitivity analysis of the new method with respect to toxicity scores, and discuss practical issues such as extending the simple algorithmic up-and-down designs.