Despite the several speedup methods proposed in the literature, the computational complexity of High Efficiency Video Coding (HEVC) video encoding is still a problem. This paper proposes a fast coding unit (CU) partition decision for use in HEVC encoders based on support vector machine (SVM)-trained offline. The SVM classifiers, features, and training procedures are described in detail, and a justification for the use of SVMs is provided. The trained classifiers are incorporated into a modified reference encoder in the form of a fast CU partition decision algorithm, which decides if the exhaustive search for the best partition is continued or terminated prematurely. Using the proposed method, an average complexity reduction of 48% is achieved with a 0.48% Bjontegaard-Delta bitrate (BD-BR) loss using the random access coding configuration, 44% reduction with a 0.62% BD-BR loss for the Low Delay B, and a 41% reduction with a 0.6% BD-BR loss for the Low Delay P configuration. We also tested our approach under constant bitrate conditions, achieving a 47% reduction in encoding time with a 1.11% loss in the BD-BR. In addition, a decision threshold adaptation is also proposed to allow adjusting the rate-distortion/complexity trade-off of our solution. With this approach, the computational complexity reduction can be varied from 34.9% (with a 0.13% loss in the BD-BR) up to 52.4% (with a 1.11% BD-BR loss) using the random access configuration. Compared with the state-of-the-art solutions, our decision scheme outperforms the related works in terms of combined rate distortion and complexity.