This paper presents a fast integer-pixel motion estimation (ME) algorithm for High Efficiency Video Coding (HEVC), which provides a strategy to speed up the search process significantly, while yielding the same quality performance as the Test Zone Search (TZSearch) scheme in HEVC Test Model (HM). Compared with the H.264/AVC, the ME process employs a more complex hybrid coding architecture and a larger size search window in HEVC, leading to great computational complexity. We utilize limited pixels of certain position in the current search range to build a quadratic model, and then shrink the search range repeatedly by analyzing the sum of absolute difference (SAD) distribution until the best motion vector (MV) is obtained. The proposed algorithm can be applied to various encoding conditions. Experimental results show that our method can save 56% of computations compared with the TZSearch scheme, with negligible decrease of coding quality.