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Tobacco epidemic which is the primary risk factor for noncommunicable diseases such as cardiovascular, cancers, diabetes and hear diseases, has been one of the most serious public health problems in the globe. It is of vital significance to control tobacco epidemic and reduce smoking rate in order to protect our health and life. For this purpose, a delayed giving up smoking model considering relapse is proposed in this research work. Local stability and existence of Hopf bifurcation are performed through taking different combinations of the two delays as bifurcation parameters. Specially, global exponential stability is proved with aid of LMI techniques. Finally, the theoretical results are verified numerically and graphically.