The properties of dc-SQUIDs with a resistively shunted inductance(Rdc-SQUID) were theoretically analyzed. The dependencies of Sv,S1/2,and dv-/da on the bias current ib for Rdc-SQUID were presented. The advantages of the high-Tc dc-SQUID magnetometer with using Rdc-SQUID have been discussed. A chip of high-Tc dc-SQUID magnetometer with modulation parameter β=4 and damping parameter γ=0.5 was designed under the conditions of the depositing and lithographic technology in laboratory. A gold thin film (≈50nm thickness and 10μm width) was deposited on the superconductive loop as the damping resistance. The theoretical values of S1/2Φ and S1/2B for the magnetometer are respectively 2.4×10-6Φ0/Hz and 200fT/Hz. Comparing the properties between dc-SQUID and Rdc-SQUID,the experimental value S1/2B,which is about 400 fT/Hz,for the magnetometer directly coupling with a 8 mm- input coil was estimated.