Lower-hybrid current drive (LHCD) experiments were carried out in the HL-1M hydrogen plasmas. The suppression of sawtooth instabilities by LHCD has been observed in the sawtoothing discharges; an improvement in the global energy confinement time of up to 20% is observed. There is an optimal rf-power range for the complete suppression of the central MHD instabilities. Possible mechanisms for the stabilization of the sawtooth instability are discussed from the measurement of inteal inductance and current profile reconstruction using an equilibrium code. A large long-lived snake-like oscillation is newly observed at the end of the sawtooth-stabilization phase of the LHCD operation in the HL-1M tokamak. It is evident that such perturbation is due to a temperature depression caused by impurity accumulation during LHCD.