Rate-distortion optimised quantisation (RDOQ) is generally utilised in video coding for achieving higher coding efficiency. To determine the optimal quantised level for each transform coefficient, it requires considerable complexity in practice to calculate rate-distortion (RD) costs from multiple candidates of quantised levels. This study proposes a fast RDOQ algorithm with low computational complexity for the latest video coding standard, the high-efficiency video coding. Instead of calculating the RD costs from two candidates of quantised levels separately, their RD cost differences were derived. A bit-rate estimation method is then used to accurately calculate the length of coding bits in the RD cost function, avoiding the high-computation-cost process of context-adaptive binary arithmetic coding. Experimental results show that, with a negligible degradation of coding performance, the proposed algorithm is faster than RDOQ by 74.6% in average.