Electroencephalogram (EEG) gives researchers a non-invasive way to record cerebral activity. It is a valuable tool that helps clinicians to diagnose various neurological disorders and brain diseases. Blinking or moving the eyes produces large electrical potential around the eyes known as electrooculogram. It is a non-cortical activity which spreads across the scalp and contaminates the EEG recordings. These contaminating potentials are called ocular artifacts (OAs). Rejecting contaminated trials causes substantial data loss, and restricting eye movements/blinks limits the possible experimental designs and may affect the cognitive processes under investigation. In this paper, a nonlinear time-scale adaptive denoising system based on a wavelet shrinkage scheme has been used for removing OAs from EEG. The time-scale adaptive algorithm is based on Stein's unbiased risk estimate (SURE) and a soft-like thresholding function which searches for optimal thresholds using a gradient based adaptive algorithm is used. Denoising EEG with the proposed algorithm yields better results in terms of ocular artifact reduction and retention of background EEG activity compared to non-adaptive thresholding methods and the JADE algorithm.