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Traditional ambient noise tomography methods using regular grid nodes are often ill posed because the inversion grids do not always represent the distribution of ray paths. Large grid spacing is usually used to reduce the number of inversion parameters, which may not be able to solve for small-scale velocity structure. We present a new adaptive tomography method with irregular grids that provides a few advantages over the traditional methods. First, irregular grids with different sizes and shapes can fit the ray distribution better and the traditionally ill-posed problem can become more stable owing to the different parametrizations. Secondly, the data in the area with dense ray sampling will be sufficiently utilized so that the model resolution can be greatly improved. Both synthetic and real data are used to test the newly developed tomography algorithm. In synthetic data tests, we compare the resolution and stability of the traditional and adaptive methods. The results show that adaptive tomography is more stable and performs better in improving the resolution in the area with dense ray sampling. For real data, we extract the ambient noise signals of the seismic data near the Garlock Fault region, obtained from the Southern California Earthquake Data Center. The resulting group velocity of Rayleigh wave is well correlated with the geological structures. High-velocity anomalies are shown in the cold southern Sierra Nevada, the Tehachapi Mountains and the Western San Gabriel Mountains. In contrast, low velocity values are prominent in the southern San Joaquin Valley and western Mojave.