The invention relates to the technical field of dynamic-response analysis of marine floating structures, and particularly to a delay function-based frequency-domain response algorithm of a marine floating structure. The algorithm comprises the following steps: S1, carrying out complex exponent decomposition on a delay function in a Cummins motion equation, and obtaining, by solving, an expressionwhich is in a Laplace domain and of the delay function; S2, obtaining, by solving, an expression which is in the Laplace domain and of a transfer function in the Cummins motion equation; S3, carryingout complex exponent decomposition on an external load in the Cummins motion equation, and obtaining, by solving, an expression which is in the Laplace domain and of the external load; and S4, calculating frequency-domain motion response. According to the algorithm, complex exponent decomposition technology is used, a delay function term in the time-domain equation is expressed as a complex exponent form of an extreme value and a residue, then the expression which is in the Laplace domain and of the delay function is obtained, and the transfer function in the Laplace domain is used as a bridgeto carry out solving with a frequency-domain load effect to obtain the frequency-domain motion response of the structure. For solving of the frequency-domain load, the algorithm uses the complex exponent decomposition technology instead of FFT (Fast Fourier Transform), overcomes a shortcoming that an external load needs to be based on the periodic harmonic assumption, and enables a periodic loadto be a special case of the algorithm.