Passengers at Heathrow Airport are regularly facing two-hour queues at passport control, it has been claimed.
Cruz suggested the lines are sending a poor message for a country trying to prove it was open for business as it prepares to leave the 28-nation European Union next year.
"What kind of message does this send, as we try to build links outside the EU?", Cruz wrote.
He also said tackling the mammoth queues should be a "top priority" for the government, dismissing the reported plan for special lanes for United Kingdom passport holders after Brexit.
British Airways' CEO Alex Cruz has called on the government to address the "border farce" which he said was leading to much longer passport control queues in the United Kingdom than "most other countries".
Mr Cruz said UK-only lines were a matter for government, but its priority should be preventing long queues now.
Current Home Office targets call for 95 per cent of passengers from the European Economic Area to wait no more than 25 minutes at passport control (45 minutes for non-EEA citizens).
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He also said that those from within the EEA wait nearly an hour.
British Airways is owned by IAG, the airline group which also operates Aer Lingus, Iberia and Vueling.
The target of 25 minutes for EEA nationals and 45 minutes for people outside that region was missed 8,928 times previous year, Cruz said, and has already been reached 6,000 times in 2018.
A number of arriving passengers at Terminal 4 were forced to wait three hours before being processed owing to "lack of staffing" during England's second-round game against Colombia on July 3.
A spokesman said: 'The vast majority of people who arrive at Heathrow get through the border within our service standards.
In response the Home Office said: 'We understand the frustration for those who have experienced longer waits and remain fully committed to working with our partners to reduce waiting times as far as is possible.
Last night, the Home Office said that 200 additional staff had been deployed at Heathrow to ease the queues...