This study shows the results of evaluating the flux noises at low frequency when the alternating current(AC) bias direct offset integrated technique(DOIT) with additional positive feedback (APF) is used in a high-Tc dc superconducting quantum interference device (SQUID). The AC-bias DOIT can reduce low-frequency noise without increasing the level of white noise because each operating point in the two voltage-flux characteristics with AC bias can always be optimum on the magnetometer in the high-Tc dc-SQUID. APF can improve the effective flux-to-voltage transfer function so that it can reduce the equivalent flux noise due to the voltage noise of the preamplifier in the magnetometer. The use of APF combined with the AC-bias DOIT reduced the noise of the magnetometer by factors of 1.5 (33µΦ0/Hz vs. 50 µΦ0/Hz) at100 Hz, 3.5 (43 µΦ0/Hz vs. 150 µΦ0/Hz) at 10 Hz, and 5.2 (67 µΦ0/Hz vs. 351 µΦ0/Hz) at 1 Hz as compared with the noise levels that were obtained with the static-current-bias DOIT. The contribution of the factors at 1 Hz is about 2 by APF and 2.6 by AC bias. The performance of improving the flux noise in the AC -bias DOIT with APF is almost equal to that of the flux locked loop (FLL) circuits in which the flux modulation uses a coupling system with a transformer and with the AC bias.