The traditional approach of fragility derivation in the principal loading directions (longitudinal & transverse) may result in an under/over estimation of system fragility. For geometrically curved bridges, it is important to consider the contribution of all the major vulnerable components to the system fragility in the critical loading direction. This article presents a multi-component and multi-loading directions system fragility estimation for a geometrically curved bridge structure. For demonstration purposes, a testbed curved bridge structure was considered, and the dynamic simulations were performed using the non-linear time history analysis (NLTHA). The seismic vulnerability was evaluated by developing the fragility functions for a set of medium to strong-intensity waveforms, applied in different loading directions. Shear strain, ductility, and distortion strain were considered as the engineering demand parameters (EDPs) for the bearing, concrete, and steel piers, respectively. For the system fragility functions, the demand dependency among the components was considered in the joint probabilistic seismic demand model (JPSDM) by utilizing the correlation coefficient matrix. It was observed that the bridge system response is highly dictated by the response of the laminated rubber bearings (LRBs). Moreover, the relative comparison of the system fragility for different loading directions suggests that the critical fragility assessment should not always be decided in the principal loading directions only.