In this paper, we present a sorting-free technique for volume rendering of an irregular volume dataset. Although the importance of our particle-based volume rendering is widely recognized, its low image quality has been pointed out. Especially when the viewing point is located near the volume dataset, the footprint of the particle may be visible. To solve the problem, we develop a sorting-free technique which does not use particles and employs a projected tetrahedra with a pre-integration. In general, a projection technique requires the visibility sorting at each viewing point. To make the technique sorting-free, we regard the volume rendering as a stochastic process in which a sampling point occurs along a viewing ray at the probability of the opacity. Thus, we develop a sorting-free approach that controls the fragment rendering by using the opacity value to calculate a rendered image. Through this approach, a projected tetrahedra technique can be successfully made sorting-free. We applied our technique to large-scale irregular volumes in order to confirm its effectiveness.