The giant converse magnetoelectric coupling (GME) was observed in the multiferroic Co40Fe40B20/(011)-0.7Pb (Mg1/3Nb2/3)O3-0.3PbTiO3 heterostructures at room temperature in this investigation. A tunability of magnetization by electric field along the [100] direction was up to-66.7% at-10 Oe bias magnetic fields. Moreover, the non-volatile magnetization switching was found after removal of bipolar electric field. The corresponding remanent magnetic states even without the assistance of bias magnetic fields were stable and could be modulated synchronously by a sequence of pulse electric fields. The 90o rotation of easy axis and non-symmetrical ferroelastic domain switching contributed to the above results. This work is of great significance in designing ultra-low power and non-volatile magnetoelectric memories and other spintronic devices at room temperature.