For many applications where High Resolution (HR) Synthetic Aperture Radar (SAR) images are required, like urban structures detection, road map detection, marine structures and ship detection etc., single-look processing of SAR images may be desirable. The G family of distributions have been known to fit homogeneous to extremely heterogeneous Polarimetric SAR (PolSAR) data very well and can be very useful for processing single-look images. The multi-look polarimetric G distribution has a limitation that it does not reduce to single-look form for (multivariate) PolSAR data. This paper presents the new single-look polarimetric G distribution, which reduces to its two well-known special forms, the single-look Kp and Gp0 distributions, when the domain of its parameters are restricted. The significance of this distribution becomes evident as it fits X- & S-band sub-meter resolution (<; 1 m2) PolSAR data (acquired over the same scene at the same time in X- & S-bands) better than the Gp0 & Kp distributions, while it fits the X-band decameter resolution (10 m2) PolSAR data as good as the Gp0 distribution. Numerical Maximum Likelihood Estimation (MLE) method for parameter estimation of multivariate G, Gp0, and Kp distributions is proposed. Simulated PolSAR data has been generated to validate the convergence and accuracy of maximum likelihood parameter estimates to values corresponding to globally maximum likelihood. A new iterative algorithm for accurate estimation of speckle covariance matrix is also proposed.