The percolation behavior of composites comprising complex-shaped particles is a recurrent problem in materials science. Previous studies focused on the symmetric particles such as spheres, ellipsoids, spherocylinders, etc. The continuum percolation of a family of single axial asymmetric ovoids with tapering parameter T and aspect-ratio c/a is studied here. The geometrical properties and numerical contact detection algorithm of these ovoids are proposed firstly. Using the Monte Carlo finite-size-scaling method, the percolation threshold phi(c) of the systems comprising congruent overlapping ovoids is further determined. For a given T, phi(c) shows an initially increasing and then decreasing trend with the increasing c/a. Moreover, the value of phi(c), at the fixed c/a decreases with the increasing [T] and this trend will be more obvious with the decreasing c/a. Finally, an analytical formula is proposed to quantify the effect of ovoid's morphology, characterized by the dimensionless excluded volume of ovoid, on the percolation thresholds. (C) 2019 Elsevier B.V. All rights reserved.