[en] Generally, by properly choosing the delay time of the pump-probe field, the harmonic yield from H₂⁺ can be enhanced due to the charge-resonance-enhanced-ionization. In this paper, through controlling the laser parameters of pump-probe pulse, the improvements of spectral continuum and atto-second pulse signal from H₂⁺ have been further investigated. For the case of controlling pump pulse, it is found that the harmonic yield of H₂⁺ can be enhanced as the pump pulse duration increases. However, as the pump wavelength increases, although the harmonic cutoff can be extended, the harmonic yield is decreased. Furthermore, when the carrier envelope phase of pump pulse is chosen to be 1.0*π, the intensity of spectral continuum can be further enhanced slightly. For the case of controlling probe pulse, it is shown that the harmonic cutoff can be extended when the probe pulse duration increases. Moreover, by properly adding a down-chirp in the probe pulse, the harmonic cutoff can be further extended, showing a broader spectral continuum with a stable intensity. Furthermore, with the introduction of inhomogeneous effect of the laser field, a larger harmonic cutoff can be found and a spectral continuum with a bandwidth of 116 eV can be obtained. Moreover, the signal of this spectral continuum is only contributed by a single harmonic emission peak. Finally, through the Fourier transformation of some selected harmonics on this spectral continuum, a single atto-second pulse with the duration of 48 as can be obtained. (authors)