The effect of dislocation on the 1/f noise current in long-wavelength infrared (LWIR) reverse biased HgCdTe photodiodes working at liquid nitrogen (LN) temperature was analyzed theoretically by using a phenomenological model of dislocations as an additional Shockley-Read-Hall (SRH) generation-recombination (G-R) channel in heterostructure. Numerical analysis was involved to solve the set of transport equations in order to find a steady state values of physical parameters of the heterostructure. Next, the set of transport equations for fluctuations (TEFF) was formulated and solved to obtain the spectral densities (SD) of the fluctuations of electrical potential, quasi-Fermi levels, and temperature. The SD of mobility fluctuations, shot G-R noise, and thermal noise were also taken into account in TEFF. Additional expressions for SD of 1/f fluctuations of the G-R processes were derived. Numerical values of the SD of noise current were compared with the experimental results of Johnson et al. Theoretical analysis has shown that the dislocations increase the G-R processes and this way cause the growth of G-R dark current. Despite the fact that dislocations increase both shot G-R noise and 1/f G-R noise, the main cause of 1/f current noise in LN cooled LWIR photodiodes are fluctuations of the carriers mobility determined by 1/f fluctuations of relaxation times. As the noise current is proportional to the total diode current, growth of G-R dark current caused by dislocations leads to the growth of noise current.