During January 1972 the second Jeff Beck Group flew to the US and joined Beck at TMI Studios in Memphis, Tennessee. Some of the songs they worked on were already in their stage act and unlike Rough and Ready they also recorded five cover songs for this album, including a new version of Ashford & Simpson's "I Can't Give Back the Love I Feel For You" and Carl Perkins's Sun Records release, "Glad All Over" (1957). The Cropper and Beck collaboration "Sugar Cane" was one of several songs written whilst in the studio. At an "end of recording party", Beck was congratulated by Don Nix on his version of "Going Down", which Nix had written and was originally released by the band Moloch in 1969.Freddie King had covered the song in 1971. The album was released in the US on 1 May 1972. The UK release was held back until 9 June the same year and tours of the UK and the US followed. There were no singles taken from this album.
Jeff Beck Group was not well received by contemporary music critics.OZ magazine's Charles Shaar Murray gave it a negative review, while Billy Walker of Sounds found it inferior to Rough and Ready, and NME's Roy Carr felt that the quality of the performances "far exceeds that of the material". In his review for Rolling Stone, John Mendelsohn was highly impressed by Beck's "genius" playing, but found it hampered by the rest of the band: "When either Bob Tench's vocals or Max Middleton's usually pleasant but seldom arresting and never-smoothly-integrated jazz piano are basking therein, Jeff Beck Group's music is mostly just dull — commonplace and predictable." Rob Mackie from the Record Mirror expressed a similar sentiment and said that listeners would not be able to tell whether they are "listening to the band led by one of Britain's best ever guitarists".
In a positive review, Chris Welch from Melody Maker hailed Jeff Beck Group as "the boldest Beck guitar we've heard for a long time" because of Beck's technical ability and suspenseful phrasing. David Hughes wrote in Disc Music Echo that "..the mood and tempo changes and you are hooked to the end". On the other hand, Robert Christgau expressed contempt for how Beck's technical abilities were praised in a 1981 review: "I agree that Beck's choppy chops occasionally surprise, but that's only because he wastes so much time refining heavy (not blues or even blooze) clichés."