The five-year-old brand, which has adopted a cyan-coloured logo in a nod to its parent companies, O2 and Tesco, is promoting its coverage and tariffs.
Tesco Mobile has replaced its four pre-pay options with a single tariff, under which calls cost 20p a minute and text messages 10p.
The tariff includes half-price calls and texts to five nominated numbers.
Customers using the tariff will be able to earn four Tesco Clubcard points for every £1 added to their mobile account.
Top-ups can be purchased at the supermarket's checkouts, by phone, online or at more than 100,000 retailers in the UK that carry the top-up logo.