Congruent lithium niobate (CLN) is the most commonly used terahertz parametric gain crystal. The terahertz-wave parametric source based on the CLN crystal has the advantages of high terahertz-wave output energy and continuous tunability, but its tuning range is relatively narrow, generally during 0.6-3 THz, which limits its practical applications. Therefore, an injection pulse-seeded terahertz-wave parametric generator based on 5% mol MgO∶CLN crystal is proposed. The terahertz-wave frequency tuning range is 1-4 THz, and the maximum output energy is 1.02 μJ at 2.0 THz. The 3 dB bandwidth of the output terahertz wave is 1.94 THz, accounting for 64.67% of the tuning range. The terahertz radiation source has the characteristics of broadband and flat gain, and has higher value in practical applications.