Studying the association between random variables is an important subject in statistical analysis. In the case of circular variables where their ranges are bounded; special type of regression models are needed. This study has shed the light on some regression models of circular variables. Due the desirable characteristics of the wrapped Cauchy distribution; a new simple linear model for circular variables with a wrapped Cauchy distribution error is proposed. The maximum likelihood estimates for model parameters are obtained via an iterative procedures and the standard error of estimates as well as their confidence intervals are obtained by bootstrap methods. The accuracy of estimates are investigated via a simulation study, where the unbiasness, consistency and robustness are verified. For illustration purposes, a real data set contains the average monthly wind directions in two main cities in the Gaza Strip has been analyzed and modeled by the proposed method.