Many of affine motion compensation techniques proposed thus far employ least-square-based techniques in estimating affine parameters, which requires a hardware structure different from conventional block-matching-based one. This paper proposes a new affine motion estimation/compensation framework friendly to block-matching-based parameter estimation, and applies it to an HEVC encoder to demonstrate its coding efficiency and computation cost. To avoid a nest of search loops, a new affine motion model is first introduced by decomposing the conventional 4-parameter affine model into two 3-parameter ones. Then, a block-matching-based fast parameter estimation technique is proposed for the models. The experimental results given in this paper show that our approach is advantageous over conventional techniques.