This paper studies the problem of wide pulse pedestal and low pulse energy of a single semiconductor saturable absorber (SESAM) mode-locked fiber laser, and reports a type of transmission/reflection composite double saturable absorber (SA) passively mode-locked ultrashort pulse fiber laser based on a linear cavity structure. By increasing the transmission of SA, the times of the light pulse passing through the transmissive SA increases in the process of one oscillation cycle. The absorbance of the absorber on the front and back edge of the optical pulse is improved. The effect of the SESAM lower modulation depth on the pulse width and single pulse energy is eliminated. The influence of dispersion and nonlinearity caused by excessive pump power is reduced, and the single pulse energy is further improved. Finally, compared to the single reflection SESAM structure with the same modulation depths, the pulse width of the composite double SA mode-locked structure is shortened from 776 fs to 732 fs and the single pulse energy is increased from 2.08 nJ to 2.49 nJ.