Recently, with the development of new-generation mobile communication systems, the demand for high data rates and large bandwidth is increasing. In this study, we proposed a second-order Raman fiber amplifier designed with two second-order pumps and four first-order pumps to amplify the C+L full-band signal light using a tellurium-based optical fiber as the transmission medium, which can effectively alleviate optical communication network challenges due to bandwidth growth. First, a simplified second-order Raman coupled wave equation is solved numerically, and then the pumping parameters of the second-order Raman fiber amplifier are optimized using a cooperative search algorithm to improve output performance. Meanwhile, the performance of first- and second-order Raman fiber amplifiers under the same pump parameter configuration is analyzed. Additionally, the influence of two key factors, that is, second-order pump optical power and fiber length on the average output gain and gain flatness of a designed second-order tellurium-based Raman fiber amplifier are investigated. Experimental results show that the average output gain of the designed second-order tellurium-based fiber Raman amplifier is 27.3601 dB and the gain flatness is 0.6601 dB in the ultrawide bandwidth range of 1530?1630 nm.