The construction of concrete filled steel tubular (CFST) arch bridge has become widespread all over the world and especially in China since 1990. This paper studies the nonlinear seismic response of a CFST arch bridge on a canyon site subjected to multi-component spatially varying ground motions. The three-dimensional (3D) finite element (FE) model of the CFST arch bridge is developed with consideration of the material and geometric nonlinearities of the arch ribs. The spatially varying ground motions with consideration of wave passage effect, coherency loss effect and local site effect are stochastically simulated based on the combined one-dimensional (1D) wave propagation theory and spectral representation method. The effects of multi-component earthquake excitations, spatial variations of ground motions and varying site conditions on the seismic response of the CFST arch bridge are analysed. Numerical results show that for a reliable seismic analysis of a CFST arch bridge, multi-component earthquake excitations with consideration of ground motion spatial variations and local soil conditions should be considered.