Active noise control is an efficient approach in dealing with unwanted acoustic disturbances. However, most of the active noise control algorithms aim to control the signal of the error sensor leading to local noise attenuation only around the error microphones. One of the approaches to enlarge the quiet zone is by restraining the derivative of the sound field around the error microphone to zero. It achieves noise cancellation not only at the error microphone but also in its vicinity. This paper proposes a time-domain adaptive algorithm to implement the spatial derivative constraint, which avoids the complex analytic acoustic calculations. Furthermore, the proposed algorithm does not require extra microphones to acquire the sound field information during control. Numerical simulations are carried out to validate the effectiveness of the proposed method.