The glass transitions of poly(methyl methacrylate) (PMMA) oligomer confined in alumina nanopores with diameters much larger than the polymer chain dimension were investigated. Compared with the case of 80 nm nanopores, PMMA oligomer confined in 300 nm nanopores shows three glass transition temperatures (from from low to high, denoted as T-g,T-lo, T-g,T-inter, and T-g,T-hi). Such phenomenon can be interpreted by a three-layer model: there exists an interphase between the adsorbed layer and core volume called the interlayer, which has an intermediate T-g. The behavior of multi-T-g parameters is ascribed to the propagation of the interfacial interaction during vitrifaction process. Besides, because of the nonequilibrium effect in the adsorbed layer, the cooling rate plays an important role in the glass transitions: the fast cooling rate generates a single T-g; the intermediate cooling rate induces three T-g values, while the ultraslow cooling rate results in two T-g values. With decreasing the cooling rate, the thickness of interlayer would continually decrease, while those of the adsorbed layer and core volume gradually increase; meanwhile, the T-g,(lo) gradually increases, T-g,T-inter almost stays constant, and the T-g,hi value keeps decreasing. In such a process, the dynamic exchanges between the interlayer and adsorbed layer, core volume should be dominant.