Dual combs are an emerging tool to obtain unprecedented resolution, high sensitivity, ultrahigh accuracy, broad bandwidth, and ultrafast data updating rate in the fields of molecular spectroscopy, optical metrology, as well as optical frequency synthesis. The recent progress in chip-based microcombs has promoted the on-chip dual-comb measuring systems to a new phase attributed to the large frequency spacing and broad spectrum. In this paper, we demonstrate proof-of-concept dual-comb generation with orthogonal polarization in a single microresonator through pumping both the transverse-electric (TE) and transverse-magnetic (TM) modes simultaneously. The two orthogonal polarized pumps are self-oscillating in a fiber ring cavity. The generated dual comb exhibits excellent stability due to the intrinsic feedback mechanism of the self-locked scheme. The repetition rate of the two orthogonal combs is slightly different because of the mode spacing difference between the TE and TM modes. Such orthogonal polarized dual-combs could be a new comb source for out-of-lab applications in the fields of integrated spectroscopy, ranging measurement, optical frequency synthesis, and microwave comb generation.