MicroRNAs are currently considered as key regulators of a wide variety of biological pathways and regulate many processes of life and obtained more and more attention in recent years. In this paper, we investigate the dynamics of gene network regulated by miR-34a (microRNA) involved in triple negative feedback loop. As we know that the p53 network involve in cancer, How the cancer arise is unclear. We investigate this negative feedback network by using mathematical model and drive the theoretical results of globally asymptotic stability and provide the sufficient conditions for the periodic oscillation. These results are propitious to understand how p53 network involved in miR-34a induces the cancer.