The photoconductive antennas pumped by femtosecond laser pulses can generate broadband terahertz pulse radiation. A femtosecond laser pulse with a slowly rising-rapidly falling-shaped pulse envelope is used to interact with a photoconductive antenna to generate broadband terahertz radiation. The law of terahertz radiation is calculated based on the Drude-Lorentz model The influence of laser pulse duration and semiconductor carrier lifetime on terahertz radiation is discussed. The research results indicate that although the energy of this shaped femtosecond laser pulse is lost, this pumping method can generate wider terahertz radiation than normal femtosecond laser pulse-pumped photoconductive antennas. This result provides a new approach for generating broadband terahertz pulse radiation based on photoconductive antennas in experiments.