We report the measurements of resistivity and magnetization under magnetic fields parallel and perpendicular to the basal plane, respectively, on a cobalt-doped Eu(Fe0.89Co0.11)2As2 single crystal. We observed a resistivity drop at Tc˜21K , which shifts toward lower temperatures under external fields, suggesting a superconducting transition. The upper critical fields near Tc show large anisotropy, in contrast with those of other “122” FeAs-based superconductors. Low-field magnetic susceptibility data also show evidence of superconductivity below 21 K. Instead of the expected zero resistance below Tc , however, a resistivity re-entrance appears at 17 K under zero field, coincident with the magnetic ordering of Eu2+ moments. Based on the temperature and field dependences of anisotropic magnetization, a helical magnetic structure for the Eu2+ spins is proposed. External magnetic fields easily change the helimagnetism into ferromagnetism with fully polarized Eu2+ spins, accompanying by disappearance of the resistivity re-entrance. Therefore, superconductivity coexists with ferromagnetic state of Eu2+ spins under relatively low magnetic field. The magnetic and superconducting phase diagrams are finally summarized for both H∥ab and H∥c .