Hi,can i ask by metro how to get to taipei national palace museum?how much is the metro fare?

Take the MRT Danshui Line to the Shilin Station and take bus R30 (Red 30 - Low-floor bus) to the museum.

Or you can take the MRT Wenhu Line to the Dazhi Station and take bus B13 (Brown 13) to the museum, alighting before the Front Facade Plaza of the museum.

Without knowing your departing place, it is hard to tell the MRT fee.