An improved pixel-based method is proposed in this paper aiming at density estimation for unidirectional crowds. It is a common situation that the crowd gathered facing towards the same orientation where hazardous events may be prone to occur due to high density, such as crowds gathered in front of a rostrum, crowds waiting at an entrance, flowing crowds in a passageway, etc. In these situations, the crowd density has a linear relationship with both the proportion of facial region to the foreground and the proportion of inner edges to the foreground edges. Based on above observations, we get a model and solve its parameters by multivariate statistical regression. The experiment shows the proposed method improves the accuracy of the commonly used pixel-based method especially for high-density crowds. Index Terms - estimation of crowd density, unidirectional crowd, statistical regression, pixel-based method