Watch my local tv on my Android device
It sounds as though you are using your TV as a media renderer for a media server (hosted on your PC or other computer device).

If that is the case, then yes, it is possible to use your android device as a media renderer for a media server. Download MediaHouse UPnP / DLNA Browser and a video player with a codec that supports your video file-types (VPlayer Video Player is the best that I've found).

If you instead meant that you wanted to stream the content provided to you from your TV service provider, then that is a bit more complicated. Generally, they do not allow this since they want you to pay some odd sum of money for an additional renderer that they own.

The process would go soemthing like this (if not otherwise allowed):


Use some kind of capturing device to record (temporarily or permenently) the video content transmitted through an appropriate cable (HDMI for example). You would theoretically need to split the signal or re-route it.
Then configure a media server on your PC to stream the recorded content.


This would not provide a stream however which would have to be in a protocol like MJPEG to work as an actual "stream". You would need something akin to an ethernet based capture card that provided a video stream over IP.