Magnetic reconnection, breaking and reorganization of magnetic field topology, is a fundamental process for rapid release of magnetic energy into plasma particles that occurs pervasively throughout the universe. In most natural circumstances, the plasma properties on either side of the reconnection layer are asymmetric, in particular for the collision rates that are associated with a combination of density and temperature and critically determine the reconnection mechanism. To date, all laboratory experiments on magnetic reconnections have been limited to purely collisional or collisionless regimes. Here, we report a well-designed experimental investigation on asymmetric magnetic reconnections in a novel hybrid collisional-collisionless regime by interactions between laser-ablated Cu and CH plasmas. We show that the growth rate of the tearing instability in such a hybrid regime is still extremely large, resulting in rapid formation of multiple plasmoids, lower than that in the purely collisionless regime but much higher than the collisional case. In addition, we, for the first time, directly observe the topology evolutions of the whole process of plasmoid-dominated magnetic reconnections by using highly-resolved proton radiography.