In the standards, LTE has been specified for speeds up to around 350 km/h. The faster a user is moving the more tricky it gets to deal with fading, Doppler effects and handovers between cells. But that speed value from the standards is just a theoretical value, to be proven in practice.
It seems Huawei has just done that when they recently demonstrated their network's capabilities to journalists during a super high speed magnetic levitation train ride from Shanghai to Shanghai airport. At speeds of 430 km/h the connection was still maintained at high throughput as reported here by CNet news. Interesting pictures of the event are available here.