Optical fibers offer convenient access to a variety of nonlinear phenomena. However, due to their inversion symmetry, second-order nonlinear effects, such as second-harmonic generation (SHG), are challenging to achieve. Here, all-fiber in-core SHG with high beam quality is achieved in a random fiber laser (RFL). The fundamental wave (FW) is generated in the same RFL. The phase-matching-condition is mainly achieved through a periodically electric field induced and the gain is enhanced through the passive spatiotemporal gain modulation and the extended fiber. The conversion needs no pretreatment and the average second-harmonic (SH) power reaches up to 10.06 mW, with a corresponding conversion efficiency greater than 0.04%. Moreover, theoretical model is constructed to explain the mechanism and simulate the evolution of SH and FW. Our work offers a simple method to generate higher brightness in-fiber SH, and may further provide new directions for research on all-fiber χ(2)-based nonlinear fiber optics and RFLs.