In this paper, we experimentally demonstrate a net bit rate of 261.7 Gbit/s in a seven-core transmission system with a Kramers–Kronig (KK) receiver. The 10 GBaud 16-level quadrature amplitude modulation (QAM) signal is transmitted over a 2.5 km seven-core fiber, and the relationship between carrier-to-signal power ratio, signal power, frequency spacing, and optical power is analyzed. Moreover, a multiple-input multiple-output (MIMO) Volterra equalization algorithm with crosstalk-dependent steps is proposed to compensate for inter-core crosstalk and impairments induced by other devices. Compared to the single-input single-output (SISO) Volterra equalizer, the CSPR can be reduced by 1.3 dB, and the received power gain can reach up to 0.7 dB.