In this article bubbly flow under the specified axial pressure gradient in a curved channel is studied numerically. To do so, a second order parallelized front-tracking/finite-difference method based on the projection algorithm is implemented to solve the governing equations including the full Navier-Stokes and continuity equations in the cylindrical coordinates system using a uniform staggered grid well fitted to the geometry concerned. In the absence of gravity the mid-plane parallel to the curved duct plane, which is the symmetry plane in the single fluid flow inside the curved duct, separates the bubbly flow into two different flow regions not interacting with each other. Twelve bubbles with diameters of 0.125 wall units are distributed in the equally spaced distances from each other. The numerical results obtained indicate that for the cases studied here, the bubbles reach the statistical steady state with an almost constant final orbital motion path due to the strong secondary field. Furthermore, the effects of different physical parameters such as Reynolds number, and curvature ratio on the flow field at the no slip boundary conditions, are investigated in detail.