Quebec VIA Rail operates a serive from Montreal to Quebec City. There is a variety of fares and discounts such as child and youth discounts, advanced purhcase discounts, OAP discounts or commuter passes.
Although the train is comfortable and fast in may not be the best option for budget travellers with one way special fares starting at CAD 50.
VIA rail runs 5 services a day between the 2 cities starting at 7am and ending at 6pm from Terminus Gare Du Palais.
For more information check out their website;
http://www.viarail.ca
