Magnetoelectric (ME) composites have received attention abidingly due to the promising potential applications in magnetic field sensor and energy harvester. In recent years, shear mode ME composite was frequently discussed with promising applications in high-frequency magnetic field with large signal-to-noise ratio. Single-crystal LiNbO3, as a lead-free piezoelectric phase with high mechanical quality factor and small dielectric constant, is suitable for achieving a large shear ME effect with large shear piezoelectric coefficient d15 or d24, and different piezoelectric coefficients can be obtained by crystal-cut transformation. The transformation rule of shear ME coefficient with transformation of LiNbO3 crystal orientation and the MHz high-frequency magnetic detection is still lacking. Furthermore, self-biased ME composite can be obtained with SrFe12O19 ribbon, which is useful for the integration and miniaturization of ME sensor. In the present work, we use a series of X-cut LiNbO3 to obtain different d15 or d16 in a stretch-shear ME composite. Piezoelectric coefficient d15 and ME coefficient E15 of Metglas/LiNbO3 composite are obtained in experiment, respectively. The results show that LiNbO3 xzt/30 has the largest d15 and E15, and the transformation rule of E15 is consistent with the coordinate transformation of d15. The structure of stretch-shear ME composite is optimized to improve the ME coefficient. Then the stretch-shear mode self-biased SrFe12O19/Metglas/LiNbO3 composite is fabricated, and shear ME response is observed under zero external direct current magnetic bias. Moreover, E15 at electromechanical resonance frequency is gained at shear-mode high frequency (0.991 MHz and 3.51 MHz). The largest ME coefficient E15 is acquired in the stretch-shear 5-foil Metglas/LiNbO3 (xzt/30) composite of 134.16 mV/(cmOe) at 1 kHz and 9.17 V/(cm Oe) at 3.51 MHz. This work is beneficial to the confirming of the corresponding rules of shear ME coefficient and LiNbO3 piezoelectric coefficient, showing that the composite possesses the potential applications in integration, miniaturization and high-frequency resonant sensor.