A dengue disease epidemic model with nonlinear incidence is formulated and analyzed. The equilibria and threshold of the model are found. The stability of the system is analyzed through a geometric approach to stability. The proposed model also exhibits backward bifurcation under suitable conditions on parameters. Our results imply that a nonlinear incidence produces rich dynamics and they should be studied carefully in order to analyze the spread of disease more accurately. Finally, numerical simulations are presented to illustrate the analytical findings.