In this talk we investigate partial regularity of a class of weak solutions of the three dimensional chemotaxis-Navier-Stokes equations, and obtain the 5/3-dimensional Hausdorff measure of the possible singular set is vanishing. The new ingredients are to establish certain type of local energy inequality of weak form and deal with the non-scaling invariant quantity of $n\ln n$. This is a joint work with Xiaomeng Chen and Shuai Li.