Travel time is an important variable that influences the hydrologic response of watersheds. Hydrologic models often do not take the variation of slope along the flow paths, i.e. profile curvature, directly into account. In this study, using a kinematic wave-based model, the effect of profile curvature on the travel time in parallel hillslopes is investigated. Also, the profiles associated with minima travel times are derived. Moreover, the range of profile curvature for which this error becomes negligible is determined. Finally, a kinematic wave-based geomorphic index is derived which considers profile curvature and plan curvature. Given that a rather similar index has been previously developed, the two indices are compared. It is concluded that there is no universal rule about which type of profile (curvature, concave or convex) has the longer travel time. In fact, this strongly depends on the degree of curvature. However, travel times for convex hillslopes are generally more than those of the straight hillslopes. In contrast, there is no consistent trend regarding the variation of travel time with the degree of curvature in concave hillslopes. Furthermore, ignoring slope variation in travel time determination may potentially cause an underestimation by up to 12% in convex hillslopes.