Collisionless shocks are produced in counter-streaming plasmas with an external magnetic field. The shocks are generated due to an electrostatic field generated in counter-streaming laser-irradiated plasmas, as reported previously in a series of experiments without an external magnetic field [T. Morita et al., Phys. Plasmas, 17, 122702 (2010), Kuramitsu et al., Phys. Rev. Lett., 106, 175002 (2011)] via laser-irradiation of a double-CH-foil target. A magnetic field is applied to the region between two foils by putting an electro-magnet (∼10 T) perpendicular to the direction of plasma expansion. The generated shocks show different characteristics later in time (t > 20ns).