In this paper, we proposed a way to realize an Er-doped random fiber laser (RFL) with a disordered fiber Bragg grating (FBG) array, as well as to control the lasing mode of the RFL by heating specific locations of the disordered FBG array. The disordered FBG array performs as both the gain medium and random distributed reflectors, which together with a tunable point reflector form the RFL. Coherent multi-mode random lasing is obtained with a threshold of between 7.5 and 10 mW and a power efficiency between 23% and 27% when the reflectivity of the point reflector changes from 4% to 50%. To control the lasing mode of random emission, a specific point of the disordered FBG array is heated so as to shift the wavelength of the FBG(s) at this point away from the other FBGs. Thus, different resonance cavities are formed, and the lasing mode can be controlled by changing the location of the heating point.