The existence of outliers in any type of data affects the estimation of models’ parameters. To date there are very few literatures on outlier detection tests in circular regression and it motivated us to propose simple techniques to detect any outliers. This paper considered the complex linear regression model to fit circular data. The complex residuals of complex linear regression model were expressed in two different ways in order to detect possible outliers. Numerical example of the wind direction data was used to illustrate the efficiency of proposed procedures. The results were very much in agreement with the results obtained by using the circular residuals of the simple regression model for circular variables.