The most challenging aspect of through-wall imaging is the presence of the wall, which suppresses the detection and localization to the obscured scatterers. Moreover, wall parameters are not known in practice; how to detect the target without prior knowledge of the wall is becoming important. Therefore, an approach is proposed to solve this problem in this paper. First, an effective clutter mitigation method based on singular value decomposition is proposed to achieve the target scattering fields. After a number of data pairs that consist of the target position and its scattering fields have been collected, the through-wall detection problem can be resolved by extracting a nonlinear relationship between them. In this way, the presence of the wall is automatically included in the nonlinear relationship, which is obtained through a training phase using a support vector machine. For a detection task, the position of the target can be estimated from this nonlinear relationship. The whole detection procedure does not require the prior knowledge of the wall. Also, it is shown that the proposed method is effective. Moreover, the impacts of training samples and signal-to-noise ratio on detection accuracy are analyzed.