We report on the generation of continuously tunable multi-cycle THz pulses with center frequencies from 0.3 to 0.8 THz in the organic nonlinear crystal, HMQ-TMS [2-(4-hydroxy-3-methoxystyryl)-1-methylquinolinium 2,-4,-6-trimethylbenzenesulfonate], by collinearly phase matched optical rectification of temporally shaped 800 nm pulses. The generation of harmonic frequency components inherent in the pulse shaper is selectively suppressed by varying the generation crystal thickness. THz pulses generated from HMQ-TMS show up to 20 times higher pulse energies compared to the benchmark inorganic THz generator ZnTe under identical conditions. The THz energy conversion efficiencies are measured to be on the order of 10(-5).