This paper proposes a fast cell traversal method for volume rendering of irregular volume datasets. All cells of an irregular volume are subdivided into a set of tetrahedral cells for our algorithm. The number of calculations required to find the intersections of a ray and irregular volume is reduced by using the exterior faces of cells rather than the ray as a basis for processing. An efficient new method of computing the integration of the brightness equation along a ray takes advantage of the linear distribution of data within a tetrahedral cell. Benchmark tests proved that the proposed method significantly improves the performance of volume rendering.