High Efficiency Video Coding (HEVC) is the next-generation video coding standard currently under development, which has demonstrated substantial bit savings (rate reduction by approximately half) compared to H.264/AVC. This paper presents the multiple sign bits hiding scheme that was adopted into the committee draft of HEVC at the 8th JCT-VC meeting. In HEVC, the quantized transform coefficients are entropy-coded in groups of 16 coefficients for each transform unit. With multiple sign bits hiding, for coefficient groups that satisfy certain conditions, the sign of the first non-zero coefficient along the scanning path is not explicitly transmitted in the bitstream and instead is inferred from the parity of the sum of all non-zero coefficients in that coefficient group at the decoder. To ensure the matching between the hidden sign and the parity of the sum of all non-zero coefficients, a parity adjustment method is employed at the encoder based on rate-distortion optimization or distortion minimization. Compared with conventional video coding schemes where quantization and coefficient coding are separately designed, the multiple sign bits hiding scheme in HEVC represents a joint quantization and coefficient coding design and provides consistent rate-distortion performance gains for all standard test sequences under standard test conditions.