Primecare, which has been employed by NHS England since July last year, also made 18 phone consultations with patients up to November.
One West Midlands GP described the cost of the deal as "extortionate".
An NHS England spokesman said Primecare had been the cheapest available service on offer.
Primecare was employed after the government allowed people to register with GPs outside of where they live in 2014.
The company was given an upfront payment of £165,253 in July, with an extra £80 agreed for each GP visit and £30 for phone consultations.
David Williams, NHS England's lead director for primary care in the West Midlands, said GPs in the West Midlands were approached to run the service before Primecare.
"With no local option we asked others for costed proposals for providing this scheme," he said.
"Primecare offered the lowest quoted price for the service that needed to be delivered."
A spokesman for Primecare said it was the choice of health commissioners to offer the money upfront, adding the firm had two GPs staffed during the week to cover the service.
"Although there were fewer service users than originally expected, the service was available for everyone registered outside their local area who may have needed a home visit or telephone consultation between July 2015 and March 2016," he said.
Coventry GP Dr Grant Ingrams, who says he is leaving the West Midlands because of workload and lack of resources, described the figure as "extortionate".
"At a time when the NHS is so short of resources, to spend so much on a private contract that's for profit is just a waste of money," he said.
A health company received more than £165,000 from the NHS in the West Midlands despite carrying out one GP callout in five months, it has emerged.