The maximum (anaerobic) swimming speed (U) of fish are limited by the length(L) of the fish's body and the temperature (T). The maximum swimming frequencyof the tail (f) is regulated by the time of muscle contraction (T_(mo)) which in turn iseffected by the size and temperature in all species of fish. An empirical formula isdeveloped here to express these relationships:u=KL/2T_(mc)The distance of each stride is equal to KL fish length (L).T_(mc)= 0.0236L^(0.4233)+0.0028 ln T -0. 0059 ln TL^(0.4233)-0.0077Where the swimming coefficient (K) is a function of the Propellent efficiency(η_p) and ratio of body wave length to body lengh (λ_b/L), propellent efficiency isrelated to wave velocity and forward speed. The relationship between the peopellentefficiency and the specific amplitude is discussed. It shows that fish adjusts its fin areato get the best efficiency with varied specific amplitude.A set of empirical formula is derived from experimental data:η_p=1/2(1+U/V)saith:=-349.30(A/L)²+66.51-2.38Cod: U/V=-19.43(A/L)²+ 4.66(A/L)²+ 0.44Mackeral:U/V = -30.33(A/L)² + 8.98(A/L) + 0.11 and Saith: U/L=0.75(f-0.088);K=0.69-0.97Cod: U/L=0.67(f+0.198); K=0.57-0.77Macheral:U/L=0.82(f-0.321);K=0.63-0.98It is pointed out that fish could greatly increase its swimming speed by reducingthe number of waves on body. For instance, fish will swim at double speed whenchanged its body wave from one complete wave to a half wave.A set of maximum swimming speed curves have given based on K =0.70 and N=1.