The new service, via Chester, Wrexham and Llandudno, is scheduled to begin on 29 May and is in addition to the present direct service which runs via Crewe.
Mr Law said: 'This is another example of the national assembly's commitment to further improving social inclusivity by bridging the gap between North and South Wales. There has been a general demand for this extra service for some time, and I am delighted that we are now able to provide funding for a year. This will allow Wales and West Passenger Trains Ltd to further develop this important link for the benefit of the whole community and particularly business customers. During this time we hope to demonstrate both the demands for the extra train and the benefits it can bring.'
Sue Essex, the new transport secretary, said: 'Since the assembly came into being last May, a tremendous amount of work has been done to improve our north-south rail links, and Peter Law's announcement today marks a highly significant point in our drive for better economic and social cohesion in Wales.
'Active partnership will be the key to achieving better rail services in Wales, and the co-operation with Wales and West on providing the extra north-south train is typical of the more collaborative approach which the assembly intends to build with the shadow strategic rail authority, with Railtrack and all train operators.'
The current Monday-Friday direct service leaves Holyhead at 05.23 via Crewe for Cardiff, arriving at 10.06. It returns from Cardiff, leaving at 17.45 and arriving at Holyhead at 22.38. Different times apply on Saturdays and Sundays.
The new service is expected to leave Cardiff at 07.10, arriving at Holyhead, via Wrexham and Chester, at 12.06. The return service will leave Holyhead at 14.36 and arrive back in Cardiff at 20.06. It will run from Monday to Saturday.
The national assembly for Wales is providing approximately£750,000 to fund this service for one timetable year, starting on 29 May, 2000.