Raman fiber laser (RFL) has been widely adopted in astronomy, optical sensing, imaging, and communication due to its unique advantages of flexible wavelength and broadband gain spectrum. Conventional RFLs are generally based on silica fiber. Here, we demonstrate that the phosphosilicate fiber has a broader Raman gain spectrum as compared to the common silica fiber, making it a better choice for broadband Raman conversion. By using the phosphosilicate fiber as gain medium, we propose and build a tunable RFL, and compare its operation bandwidth with a silica fiber-based RFL. The silica fiber-based RFL can operate within the Raman shift range of 4.9 THz (9.8-14.7 THz), whereas in the phosphosilicate fiber-based RFL, efficient lasing is achieved over the Raman shift range of 13.7 THz (3.5-17.2 THz). The operation bandwidths of the two RFLs are also calculated theoretically. The simulation results agree well with experimental data, where the operation bandwidth of the phosphosilicate fiber-based RFL is more than twice of that of the silica fiber-based RFL. This work reveals the phosphosilicate fiber's unique advantage in broadband Raman conversion, which has great potential in increasing the reach and capacity of optical communication systems.