360-degree　images/videos　have　been　dramatically　increasing　in　recent　years.　The　characteristic　of　omnidirectional-view　results　in　high　resolution　of　360-degree　images/videos,　which　makes　them　difficult　to　be　transported　and　stored.　To　deal　with　the　problem,　video　coding　technologies　are　used　to　compress　the　omnidirectional　content　but　they　will　introduce　the　compression　distortion.　Therefore,　it　is　important　to　study　how　popular　coding　technologies　affect　the　quality　of　360-degree　images.　In　this　paper,　we　present　a　study　on　both　subjective　and　objective　quality　assessment　of　compressed　virtual　reality　(VR)　images.　We　first　build　a　compressed　VR　image　quality　(CVIQ)　database　including　16　reference　images　and　528　compressed　ones　with　three　prevailing　coding　technologies.　Then,　we　propose　a　multi-channel　convolution　neural　network　(CNN)　for　blind　360-degree　image　quality　assessment　(MC360IQA).　To　be　consistent　with　the　visual　content　seen　in　the　VR　device,　we　project　each　360-degree　image　into　six　viewport　images,　which　are　adopted　as　inputs　of　the　proposed　model.　MC360IQA　consists　of　two　parts,　a　multi-channel　CNN　and　an　image　quality　regressor.　The　multi-channel　CNN　includes　six　parallel　hyper-ResNet34　networks,　where　the　hyper　structure　is　used　to　incorporate　the　features　from　intermediate　layers.　The　image　quality　regressor　fuses　the　features　and　regresses　them　to　final　scores.　The　experimental　results　show　that　our　model　achieves　the　best　performance　among　the　state-of-art　full-reference　(FR)　and　no-reference　(NR)　image　quality　assessment　(IQA)　models　on　the　CVIQ　database　and　other　available　360-degree　IQA　database.