A fast vector multiplication and accumulation circuit is applied to an artificial neural network accelerator and configured to calculate an inner product of a multiplier vector and a multiplicand vector. A scheduler is configured to arrange a plurality of multiplicands of the multiplicand vector into a plurality of scheduled operands according to a plurality of multipliers of the multiplier vector, respectively. A self-accumulating adder is signally connected to the scheduler and includes a compressor, at least two delay elements and at least one shifter. The compressor is configured to add the scheduled operands to generate a plurality of compressed operands. The at least two delay elements are connected to the compressor. The shifter is configured to shift one of the compressed operands. An adder is signally connected to the output ports of the compressor so as to add the compressed operands to generate the inner product.