La Parrilla's closed in SA1 and Mumbles.
A statement on the companies website says it comes after tough times in the sector.
Their sister restaurant La Braseria is unaffected and will remain open.
The statement says: 'Regrettably, we have made the very hard decision to close our two La Parrilla restaurants in SA1 and Mumbles from today, the 15th January.
'We are contacting customers with bookings to advise them and offer alternate arrangements at La Braseria, our sister restaurant that is unaffected and remains open.
'Whilst the decision to close both La Parrilla restaurants has been extremely difficult, it comes after a long period of reflection on how we could strengthen and evolve our family-run company against a backdrop of unprecedented tough times for the restaurant sector in the UK.
'We are extremely grateful to all our amazing staff and suppliers at both of the La Parrilla restaurants and would like to thank all our La Parrilla customers for their custom over the years.
'If you have a La Parrilla gift voucher you will still be able to use it under the same terms at La Braseria.
'To discuss existing bookings or gift vouchers please call 07825 983 196 or contact La Braseria on 01792 469 683'