We present development of a high-energy Mamyshev oscillator (MO) and demonstrate high-efficiency pulse compression of the MO using a state-of-the-art anti-resonant hollow-core fiber (AR-HCF). The MO generates 2 ps pulses at 1050 nm with a pulse energy up to 527.2 nJ. The in-house fabricated AR-HCF provides a low-loss (<0.0013 dB/m) transmission window that covers the entire spectra of the MO output, enabling an overall transmission efficiency up to 90.4 %. As a linear compressor, the AR-HCF significantly shortens the output pulses of the MO without spectral distortion, yielding high-quality pulses with a pulse width of 55.9 fs. The combing technologies of MO and AR-HCF offer great advancement in generation and delivery of high-energy ultrashort pulse, providing good potential for real-life applications.