Laser control on the generations of the molecular high-order harmonic generation (MHHG) and the isolated attosecond pulse (IAP) from H2+ have been theoretically investigated through solving the non-Bohn–Oppenheimer time-dependent Schrödinger equation. It is found that (i) in the middle laser intensity (i.e., I = 4.0 × 1014 W/cm2), the contribution from negative-H to the MHHG is higher than that from the positive-H. With the decrease (i.e., I = 2.0 × 1014 W/cm2) or the increase (i.e., I = 7.0 × 1014 W/cm2) in laser intensity, the asymmetric contributions from the two H nuclei to the MHHG are decreased. (ii) Pulse duration investigation shows that the distributions of the MHHG in two H nuclei present similar contributions as the pulse duration is enhanced. (iii) Laser phase investigation shows that when the laser phase is chosen from 0.0π to 0.6π and from 1.7π to 2.0π, the contribution from the negative-H plays the main role in MHHG. When the laser phase is chosen from 0.7π to 1.6π, the contribution from the positive-H to the MHHG is remarkably enhanced and becomes greater than that from the negative-H. The time–frequency analyses of the MHHG and the time-dependent wave function are shown to explain the harmonic emission process and the electron motion in H2+. (iv) With the introduction of one or two half-cycle controlling pulses, the cutoff and the intensity of the MHHG spectra can be controlled. Finally, by selecting the harmonics generated during a single harmonic emission event, an IAP with the full width at half maximum of 48 as can be produced.