High-dielectric-constant and low-loss ceramics in the (Mg1-xCox)Ta2O6 solid solutions have been prepared using the conventional mixed oxide route and their microwave dielectric properties have been investigated. The X-ray diffraction patterns as well as the measured lattice parameters indicated the (Mg1-xCox)Ta2O6 ceramics tended to form a complete solid solution with a trirutile structure. In comparison with that of simple MgTa2O6, an enhanced grain growth can be achieved by substituting Mg with 0.05 mol% Co. It also leads to an increase in both the epsilon(r) and Q x f values of the ceramics. The specimen with x=0.05 possessed a combination of microwave dielectric properties: epsilon(r)similar to 30.67, the Q x f similar to 106 200 GHz, and tau(f)similar to 42.9 ppm/degrees C.