An effective quaternary catalyst consisting of trialkyl aluminum, phosphoric acid, electron donor, and water for ring-opening polymerization of epichlorohydrin (ECH), as well as its copolymerization with ethylene oxide (EO), propylene oxide (PO), and allyl glycidyl ether (AGE) to obtain elastomers, were studied. We investigated the optimum composition for the quaternary catalyst; the character of the catalyst; the reactivity of the four alkylene oxides during homopolymerization and copolymerization; the behavior of ECH, EO, and PO during terpolymerization; and glass transition temperatures of the copolymer and terpolymers. The results showed that the nitrogen-containing electron donors are suitable as the third component, whereas oxygen-containing electron donors are not. Water as the fourth component can increase the molecular weight of the homopolymer and copolymers of ECH. According to the polymerizability of tetrahydrofuran with the quaternary catalyst and the reactivity ratios of the four alkylene oxides, the quaternary catalyst was assumed to be of a coordinated anionic type. The reactivity ratios for these four alkylene oxides were determined to be EO > PO > AGE > ECH. They were verified by terpolymerization of ECH, EO, and PO. The glass transition temperature of the terpolymer exhibits a minimum value at nearly 3:1 molar ratio of PO to EO, when the molar ratio of ECH used is constant at the beginning of terpolymerization.