Is there a speed train from Zhongshan to Beijing?

No, there is no direct train service between these two cities. Thus you are suggested to take a bullet train to Guangzhou South Railway Station first. Then transfer to the train to Beijing.

There is a high speed train from Zhongshan to Beijing now. Only at Mon. Fri. Sat. Sun. Leave at 19:35 in Zhongshan Railway Station(the one near Haotou not the one near Shiqi,you can take Bus No.002 005 011 018). The destination is Beijingxi(Beijing West) Station. It costs around 800-1500 CNY (120-240 USD), depending on the seat you want.