Based on the compact and efficient optically pumped terahertz laser(OPTL) technology, an optically pumped terahertz fiber laser(OPTFL) based on a negative curvature hollow core fiber was designed. This OPTFL used a hollow-core fiber with polymethylpentene(PMP) material as operation gas chamber and was filled with methanol gas and pumped by 9P(36) continuous-wave(CW) CO2 laser. Based on rate equations and the transmission theory in hollow core fiber, factors affecting the output characteristics of OPTFL were analyzed. By investigating inner microstructure of hollow-core fiber, a negative curvature hollow-core fiber for efficiently transmitting terahertz waves was proposed. Considering the designed negative curvature hollow-core fiber, the feasibility of long cavity OPTFL was analyzed. Theoretical calculations showed that by appropriately increasing the cavity length of the proposed OPTFL, the terahertz output power was expected to reach the order of 100 milliwatts with optimal operating conditions. The results provide a new method for the OPTFL with high power and high performance.