In this paper, transmission of orthogonal chirp division multiplexing (OCDM) based on asymmetric pair mapping over a seven core fiber is proposed. High-order 32 quadrature amplitude modulation (QAM) is reduced to quadrature phaseshift keying (QPSK) and 8 QAM signal employing asymmetric pair mapping, which will not affect the rate of the system. Combined with geometric shaping (GS), the average transmission power is successfully lowered, realizing signal damage suppression. In order to verify the performance of the proposed asymmetric pair mapping scheme, a 140 Gb/s asymmetric pair mapping OCDM signal transmission over 2 km seven core fiber is experimentally demonstrated. The experimental results show that the proposed transmission scheme has the best performance when the power distribution ratio (PDR) is 4 dB. Meanwhile, compared with GS 32 QAM with QPSK+rectangle 8 QAM, GS 32 QAM with QPSK+star 8 QAM and GS 32 QAM, the proposed asymmetric pair mapping OCDM signal has improved by 1.55dB, 1.45dB, and 0.7dB, respectively. It has a wide range of applications in the future optical transmission system due to its outstanding performance in the suppression of high-order modulation signal degradation.