Nonlinear and non-stationary ground penetrating radar (GPR) data for geophysics exploration are often mixed with various complex noise sources, such as random and coherent noise. Those complex noise sources are introduced by the acquisition system and other sources of measurement uncertainty. The data sets which are contaminated by the above noises have a serious influence on the accurate extraction of weak reflected signals and the effective identification of diffracted wave hyperbolic coaxial characteristics. The ignorance of the influence of noise will cause great errors in the interpretation of GPR data and the subsequent migration imaging with full waveform. The curvelet transform not only is related to position and frequency as compared with the wavelet transform, but also is controlled by the translation angle. With such a unique advantage, curvelets are used for ground roll whitening, coherent noise denoising and separation of overlapping events. The traditional curvelet transform denoising with a hard threshold function needs to give a reasonable threshold function control coefficient according to the noise level of GPR data. As a result, an appropriate choice of a hard threshold is a basic requirement, and this presents a challenging task in curvelet denoising. To overcome these shortcomings, an self-adaptive threshold function for GPR data denoising with curve transform is proposed in this paper. For detailing the reasonable control coefficient of the threshold function, the complex block threshold function algorithm is used to analyze the distribution of peak-signal-to-noise ratio value of the noisy synthetic GPR data contaminated with random and coherent noise by using the traditional threshold function curvelet transform. Based on the high order statistical theory, the accuracy distribution of the curvelet coefficient for useful signals in scale and rotation direction are correlatively stacked and determined by using the statistical self-adaptive function. And then the threshold range of noise removal components is given by the statistical self-adaptive function. The effectiveness of the proposed denoising algorithm for the noisy synthetic contaminated with different types of noise (i.e., Gaussian random and coherent), and field GPR data is demonstrated by comparing the denoising results via curvelet transform with those from traditional thresholding function. The presented denoising results by the statistical self-adaptive function is helpful and instructive for the accurate inference and interpretation of complex GPR data.