Attosecond-resolution molecular high-order harmonic generation (MHHG) and isolated attosecond pulse generation (IAP) from H2+ has been theoretically investigated through solving the Non-Bohn-Oppenheimer (NBO) time-dependent Schrödinger equation (TDSE). Results show that the harmonic spectra present the asymmetric distribution to the two H nuclei. Particularly, when the laser field is larger than zero (E(t)>0.0), the harmonic generation from the negative-H is higher than that from the positive-H; while when the laser field is smaller than zero (E(t)<0.0), the harmonic generation from the positive-H is higher than that from the negative-H. Further, by properly adding a half-cycle pulse, the harmonic cutoff and the intensities of the harmonic spectra from the two H nuclei can be controlled. As a result, a 237eV super-bandwidth and a 43 as pulse can be produced.