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Taking the 3-3-1 models (with $SU(3)_c \otimes SU(3)_L \otimes U(1)_Y$ gaugegroup) as examples, we study that a class of new physics models with extendedgauge group could undergo one or several first-order phase transitionsassociated with the spontaneously symmetry breaking processes during theevolution of the universe, which can produce detectable phase transitiongravitational wave (GW) signals at future GW experiments, such as LISA, BBO,DECIGO, SKA and aLIGO. These GW signals can provide new sources of GWs withdifferent peak frequencies, and can be used to probe the evolution history ofthe universe.

Probing the gauge symmetry breaking of the early universe in 3-3-1 models and beyond by gravitational waves