In this research, the dynamic response of a slightly curved bridges under moving mass load is studied using an analytical approach. A solution method similar to the method of successive approximation has been used. The method has been exemplified for the special values of the variables. The effects of some variables have been specifically investigated. The results reveal that the inertial, centripetal and Coriolis forces must be involved in the analysis especially when the slightly curved bridges under moving loads with high speed are examined. Depending on the convexity and concavity of the initial curve, the effects of these forces become different. In a curved bridge, the moving mass affects the bridge more than that in a straight bridge with increasing the velocity of the moving mass. It has been observed that the forced vibration of the bridge is strongly influenced by the velocity of the moving mass. Many figures have been plotted to show clearly the effects of the variables.