We present a Bayesian adaptive design for dose finding in oncology trials with application to a first-in-human trial. The design is based on the escalation with overdose control principle and uses an intermediate grade 2 toxicity in addition to the traditional binary indicator of dose-limiting toxicity (DLT) to guide the dose escalation and de-escalation. We model the dose-toxicity relationship using the proportional odds model. This assumption satisfies an important ethical concern when a potentially toxic drug is first introduced in the clinic; if a patient experiences grade 2 toxicity at the most, then the amount of dose escalation is lower relative to that wherein if this patient experienced a maximum of grade 1 toxicity. This results in a more careful dose escalation. The performance of the design was assessed by deriving the operating characteristics under several scenarios for the true MTD and expected proportions of grade 2 toxicities. In general, the trial design is safe and achieves acceptable efficiency of the estimated MTD for a planned sample size of twenty patients. At the time of writing this manuscript, twelve patients have been enrolled to the trial.