Various methods have been studied to construct a fuzzy regression model in order to present a fuzzy relation between a dependent variable and an independent variable. However, in the fuzzy regression analysis the value of the center point of estimated fuzzy output may be either greater than the value of the right endpoint or smaller than the value of the left endpoint. In the case, we cannot predict the fuzzy output properly. This paper presents sufficient conditions to construct the fuzzy regression model using several methods investigated by some authors and then introduces the censored fuzzy regression model using the censored samples to manipulate the problem of crossing of the center and the end points of the estimated fuzzy number. Examples show that the censored fuzzy regression model is an extension of the fuzzy regression model and also it improves the problem of crossing.