The scaling of traditional complementary metal oxide semiconductor (CMOS) device is reaching its physical limit, and alternative emerging devices are being explored as possible CMOS substitutes. One of the most promising device technologies is nano-magnetic logic (NML), which is an energy-efficient computing paradigm. The inherent nonvolatility and low energy consumption make NML device possess wide application perspectives. The basic element of multiferroic NML is a sub-100 nm sized single domain magnet. Generally, the x-y plane determines the in-plane dimension, while the z direction indicates the thickness of nanomagnet. Classical binary logic states 0 and 1 are encoded in two stable magnetization orientations along the easy axis (major axis) of the elliptical nanomagnet, while the hard axis (minor axis) refers to null logic. In order to propagate logic bits between the neighbor nanomagnets, one requires a clock that periodically flips every magnet's magnetization along the hard axis simultaneously, and the dipole-dipole interaction between the neighbors will force the magnet into the correct orientation along the easy axis, and thus the logic bit propagates unidirectionally. In multiferroic NML, the majority gate is a basic element of nanomagnet logcal circuit. In this paper, the three-dimensional switching dynamic model of a multiferroic nanomagnetic majority gate is established, and its magnetization dynamics is simulated by solving the Landau-Lifshitz-Gilbert equation with considering the thermal fluctuation effects. The majority gate is implemented with dipole-coupled two-phase (magnetostrictive/piezoelectric) multiferroic elements and is simulated by using different strain clocks and changing the input. It is found that the majority gate works efficiently and correctly when receiving new input. It is also found that the optimal time interval of stress releasing between central nanomagnet and output nanomagnet is 0.1-0.2 ns. Removing stress earlier will reduce the success rate of the majority gate operation while the work frequency increases. The reason behind the phenomenon may be that removing stress earlier results in weak dipole-coupled interaction, which cannot overcome the shape anisotropy. These findings are beneficial to the design of multiferroic logic circuit.