We demonstrate Bose-Einstein condensation of rubidium atoms in a simple low-power magnetic trap. This trap combines the quadrupole with the Ioffe configuration (QUIC trap) and consists of just three coils. Magneto-optically trapped 87Rb atoms are first loaded into the linear trapping potential of a magnetic quadrupole, which is then converted into the parabolic geometry of an Ioffe trap. During this process two spherical quadrupole traps with perpendicular axes merge and the trapped atomic cloud moves close to the magnetic field producing coils, resulting in tight confinement of the atoms while the power dissipation of the trap remains low. The magnetically trapped atoms are cooled to below the phase transition of Bose-Einstein condensation by rf-induced evaporation.