In this paper, the problem of adaptive radar detection is studied where the target is embedded in the clutter and noise-like jamming environment. We consider that two kinds of training datasets can be used and establish the detection problem as a binary hypothesis test. According to the suboptimal detection criterion, generalized likelihood ratio test (GLRT), two detectors are derived by using different design procedures. Since the closed-form solution of joint maximization to the unknown parameters is difficult to obtain, the circular optimization method is exploited. It is indicated that the demand of the designed detector for the number of the second kind of training data with the same statistical distribution as the cell under test can be less than the channel dimension. Finally, the performance is analyzed with the simulation data, proving the effectiveness of the proposed method.