Noise estimation is crucial in many image processing algorithms such as image denoising. Conventionally, the noise is assumed as a signal-independent additive white Gaussian process. However, for the real raw data of image sensor, the present noise should be practically modeled as signal dependent. In this paper, we propose an effective and fast image sensor noise estimation method for a single raw image. The noise model parameters are estimated via constrained weighted least squares (WLS) fitting on a number of data samples, each of which is generated from a group of weakly textured patches. Specifically, we first design a fast scheme for selecting weakly textured patches, with the guidance of image histogram. To robustly fit the data samples, we then explicitly account for the credibility of each sample by measuring the texture strength of the grouped patches. The image sensor noise estimation is finally formulated as a constrained WLS optimization problem, which can be solved efficiently. Experimental results demonstrate that our method could run much faster than the existing schemes, while retaining the state-of-the-art estimation performance.