We have enhanced the tunability of a terahertz-wave parametric generator using $\mathrm{MgO}\text{:}{\mathrm{LiNbO}}_3$ pumped by a subnanosecond, passively Q-switched, microchip Nd:YAG laser. This pump source allows high-intensity pumping without damage to the nonlinear crystal and generates a narrow linewidth and tunable terahertz wave with injection seeding by an external cavity diode laser for the idler wave. The high-intensity pumping causes a gain curve broadening of the terahertz-wave parametric generation, especially in the high-frequency region. We obtained an output terahertz wave with a tuning range of $0.9–3\mathrm{THz}$ ( $100–330\mathrm{\mu m}$ ), a peak power of $100\mathrm{mW}$ , and a linewidth of less than $10\mathrm{GHz}$ . This room temperature operated, palm-sized source promises to be a widely tunable terahertz-wave source that is suited to a variety of applications.