In　this　paper,　the　complicated　dynamics　and　multi-pulse　homoclinic　orbits　of　a　two-degree-of-freedom　parametrically　excited　nonlinear　nano-oscillator　with　coupled　cubic　nonlinearities　are　studied.　The　damping,　parametrical　excitation　and　the　nonlinearities　are　regarded　as　weak.　The　averaged　equation　depicting　the　fast　and　slow　dynamics　is　derived　through　the　method　of　multiple　scales.　The　dynamics　near　the　resonance　band　is　revealed　by　doing　a　singular　perturbation　analysis　and　combining　the　extended　Melnikov　method.　We　are　able　to　determine　the　criterion　for　the　existence　of　the　multi-pulse　homoclinic　orbits　which　can　form　the　Shilnikov　orbits　and　give　rise　to　chaos.　At　last,　numerical　results　are　also　given　to　illustrate　the　nonlinear　behaviors　and　chaotic　motions　in　the　nonlinear　nano-oscillator.