Background: Various dose-finding clinical trial designs, including the continual reassessment method (CRM), dichotomize toxicity outcomes based on prespecified dose-limiting toxicity (DLT) criteria. This loss of toxicity information is particularly inefficient due to the small sample sizes in phase I trials, especially when Common Terminology Criteria for Adverse Events (CTCAE v4.0) are an established ordinal toxicity grading classification already used in the clinical practice. Purpose: The purpose of this simulation study is to incorporate ordinal toxicity grades as specified by CTCAE v4.0 using a continuation ratio (CR) model in the likelihood-based CRM. Methods: This simulation study compares the CR model design to the dichotomous CRM as well as an ordinal CRM that implements the proportional odds (PO) model. We compare six scenarios for model performance based on various safety and efficiency criteria and consider a range of dose-toxicity relationship models, including CR models, PO models, and models that violate the PO assumption. Results: The ordinal CRM performs as well as the dichotomous CRM in all scenarios considered, especially in situations where the starting dose is overly toxic, the ordinal designs show slight improvement in the estimation of the maximum tolerated dose (MTD) and fewer median patients exposed to excessively toxic dose levels as compared to the binary CRM. We also find slight discrepancies in the performance between the PO model and CR model; however, the differences were not substantial enough to strongly recommend one model over the other.Limitations: The CR model design does require slightly more input from clinical investigators prior to the start of the trial as compared to the dichotomous CRM. Investigators must specify the distribution of toxicity grades at the expected dose levels for a 10% and 90% DLT rate in this CR design. However, an R package will help with the implementation of this ordinal design. Conclusions: While the ordinal designs did not perform significantly better than the binary counterpart, we were able to incorporate maximal toxicity information available into a feasible dose-finding design without compromising overall design performance.