The human brain cortex is a highly convoluted sheet. Mapping of the cortical surface into a canonical coordinate space is an important tool for the study of the structure and function of the brain. Here, we present a technique based on least-square conformal mapping with spring energy for the mapping of the cortical surface. This method aims to reduce the metric and area distortion while maintaining the conformal map and computation efficiency. We demonstrate through numerical results that this method effectively controls metric and area distortion, and is computational efficient. This technique is particularly useful for fast visualization of the brain cortex.