The cobalt-carbon co-doped NaZn13-type compound LaFe10.95Co0.65Si1.4C0.15 (LFCSC) is one of the most promising candidates for room-temperature working substance in magnetic refrigerator due to its many excellent properties such as large reversible entropy, low cost, and short annealing time. However, owing to the narrow temperature regions of magnetic phase transition in LFCSC, the operation-temperature window for magnetic refrigeration is limited, which restricts its actual application to some extends. In this paper, it is shown that the application of high-pressure to LFCSC during annealing can tailor atomic environment and magnetic transition, which leads to a strongly expanded phase transition temperature range in LFCSC. This broadening behavior can be well understood by importing the magnetoelastic interaction of localized magnetic moments into a microscopic model. The refrigeration performance of the high-pressure annealed sample with wide phase transition temperature range is enhanced according to the relative cooling power (RCP). On the contrary, temperature averaged entropy change (TEC) exhibits a weakened value in the high-pressure annealed sample, which suggests that the magnetic cooling performance could not be effectively improved by simply expanding the phase transition temperature range in the second-order phase transition materials. However, high-pressure annealing would be helpful to the magnetic refrigeration performance for the first-order phase transition materials.