Wing asymmetries can be found in real insects and flapping-wing micro air vehicles. This paper investigates some characteristics, including the trim conditions, power requirements and passive open-loop dynamics of an insect model with the asymmetry in wing mass in low-speed flight. The motion of the insect model is obtained through a simulation framework that couples an unsteady vortex-lattice method and a multibody dynamics code. The results show that a heavier wing has to be moved with a larger stroke amplitude to compensate for the wing mass asymmetry. The power required by the heavier wing is also found greater. Moreover, we can observe the asymmetries in lateral dynamics while comparing dynamic responses due to rightward and leftward gust disturbances.