The company, which has struggled financially in recent years, had previously said it was weighing up its options.
Now it has decided that cancelling its Aim listing is in the “best interests of the company” and will hold an extraordinary general meeting on June 8 to seek shareholder approval.
In a statement All Leisure said it had already been told that directors and shareholders representing around 76.1% of ordinary shares would vote in favour of cancelling the listing.
Although All Leisure made a small profit in its most recent financial year, it has struggled under the weight of geopolitical problems in some of its destinations.