We demonstrate a long-term operation with reduced phase noise in the carrier-envelope-phase (CEP) stabilization process by employing a double feedback loop and an improved signal detection in the direct locking technique [Opt. Express 13, 2969 (2005)]. A homodyne balanced detection method is employed for efficiently suppressing the dc noise in the f-2f beat signal, which is converted into the CEP noise in the direct locking loop working at around zero carrier-envelope offset frequency (f(ceo)). In order to enhance the long-term stability, we have used the double feedback scheme that modulates both the oscillator pump power for a fast control and the intracavity-prism insertion depth for a slow and high-dynamic-range control. As a result, the in-loop phase jitter is reduced from 50 mrad of the previous result to 29 mrad, corresponding to 13 as in time scale, and the long-term stable operation is achieved for more than 12 hours.