Asiamah was elected as the member of parliament for the Atwima Mponua constituency of the Ashanti Region of Ghana for the first time in the 2004 Ghanaian general elections. He won on the ticket of the New Patriotic Party. His constituency was a part of the 36 parliamentary seats out of 39 seats won by the New Patriotic Party in that election for the Ashanti Region. The New Patriotic Party won a majority total of 128 parliamentary seats out of 230 seats. He was elected with 30,012 votes out of 44,217 total valid votes cast equivalent to 67.9% of total valid votes cast. He was elected over John Macitse Oduro H. of the National Democratic Congress and Stephen Osei Bossman of the Convention People's Party. These obtained 30.5% and 1.7% respectively of total valid votes cast.
