Experiments of suppressing fast-ion-driven MHD instabilities such as energetic particle modes (EPMs) and global Alfven eigenmodes (GAEs) have been made using a second harmonic x-mode electron cyclotron heating and current drive (ECCD) in the helical-axis heliotron device, Heliotron J. ECCD experiments show that the GAEs destabilized by fast ions of neutral beam injection with the observed frequency around 140 kHz are fully stabilized, and the EPMs with the observed frequency around 90 kHz are suppressed when the EC-driven plasma current flowing in the counter direction reaches approximately 0.7 kA. The low magnetic shear under the vacuum condition is modified into positive magnetic shear when counter-ECCD is applied, and the amplitude of GAEs and EPMs decreases with an increase in EC-driven plasma current. These results indicate that magnetic shear plays a key role in controlling GAEs as well as EPMs. The comparison of the calculation of shear Alfven spectra with experimental results shows that the increasing continuum damping rate with an increase in local magnetic shear by EC-driven current is important for both EPMs and GAEs. Moreover, the increase in plasma current leads to the inward movement of GAEs. This effect would also contribute to suppression of GAEs because the continuum damping rate increases more and more toward the core. Steady ECH is also found experimentally to be effective for controlling the amplitude of both GAEs and EPMs. The amplitude of EPMs, and especially for GAEs, decreases with an increase in the ECH power under fixed density conditions.