In this paper, an efficient multiple-precision floating-point fused multiply-add (FMA) unit is proposed. The proposed FMA supports not only single-precision, double-precision, and quadruple-precision operations, as some previous works do, but also half-precision operations. The proposed FMA architecture can execute one quadruple-precision operation, or two parallel double-precision operations, or four parallel single-precision operations, or eight parallel half-precision operations every clock cycle. In addition to the support of normal FMA operations, the proposed FMA also supports mixed-precision FMA operations and mixed-precision dot-product operations. Specifically, the products of two lower precision multiplications can be accumulated to a higher precision addend. By setting the operands of one multiplication to zeros, the proposed FMA can also perform mixed-precision FMA operations. Support for mixed-precision FMA and mixed-precision dot-product is newly added but it only consumes 6.5 percent more area compared to a normal multiple-precision FMA unit. Compared to the state-of-the-art multiple-precision FMA design, the proposed FMA supports more floating-point operations such as half-precision FMA operations and mixed-precision operations with only 10.6 percent larger area.