Robot-assisted fruit harvesting has been a critical research direction supporting sustainable crop production. One important determinant of system behavior and efficiency is the end-effector that comes in direct contact with the crop during harvesting and directly affects harvesting success. Harvesting avocados poses unique challenges not addressed by existing end-effectors (namely, they have uneven surfaces and irregular shapes grow on thick peduncles, and have a sturdy calyx attached). The work reported in this paper contributes a new end-effector design suitable for avocado picking. A rigid system design with a two-stage rotational motion is developed, to first grasp the avocado and then detach it from its peduncle. A force analysis is conducted to determine key design parameters. Preliminary experiments demonstrate the efficiency of the developed end-effector to pick and apply a moment to an avocado from a specific viewpoint (as compared to pulling it directly), and in-lab experiments show that the end-effector can grasp and retrieve avocados with a 100% success rate.