This paper reports the generation of fundamental solitons and third-order solitons in an erbium-doped fiber laser (EDFL) by a Cr2Ge2Te6-polyvinyl alcohol (CGT-PVA) saturable absorber (SA). Stable fundamental solitons at 1559.09 nm at a repetition frequency of 5.1 MHz were detected, and third-order solitons with a maximum output power of 6.807 mW and narrowest monopulse duration of 615.2 fs were obtained under a repetition frequency of 15.3 MHz by changing pump power. To the best of our knowledge, it is the first time to achieve a Q-switched pulse with a minimum pulse duration of 2.2 µs and maximum single pulse energy of 12.11 nJ in EDFL based on CGT-PVA SA after reducing the cavity length. Its repetition rate monotonically increased from 18.8 kHz to 61.8 kHz with a tuning range of about 43 kHz. The experimental results sufficiently demonstrate that CGT has enormous potential as an ultrafast photonics device.