Mode-division multiplexing (MDM) transmission systems utilizing few-mode fibers (FMF) have been intensively explored to sustain continuous traffic growth. The key challenges of MDM systems are inter-modal crosstalk due to random mode coupling (RMC), and largely-accumulated differential mode group delay (DMGD), whilst hinders mode-demultiplexer implementation. The adaptive multi-input multi-output (MIMO) frequency-domain equalization (FDE) can dynamically compensate DMGD using digital signal processing (DSP) algorithms. The frequency-domain least-mean squares (FD-LMS) algorithm has been universally adopted for high-speed MDM communications, mainly for its relatively low computational complexity. However, longer training sequence is appended for FD-LMS to achieve faster convergence, which incurs prohibitively higher system overhead and reduces overall throughput. In this paper, we propose a fast-convergent single-stage adaptive frequency-domain recursive least-squares (FD-RLS) algorithm with reduced complexity for DMGD compensation at MDM coherent receivers. The performance and complexity comparison of FD-RLS, with signal-PSD-dependent FD-LMS method and conventional FD-LMS approach, are performed in a 3000 km six-mode transmission system with 65 ps/km DMGD. We explore the convergence speed of three adaptive algorithms, including the normalized mean-square-error (NMSE) per fast Fourier transform (FFT) block at 14–30 dB OSNR. The fast convergence of FD-RLS is exploited at the expense of slightly-increased necessary tap numbers for MIMO equalizers, and it can partially save the overhead of training sequence. Furthermore, we demonstrate adaptive FD-RLS can also be used for chromatic dispersion (CD) compensation without increasing the filter tap length, thus prominently reducing the DSP implementation complexity for MDM systems.