| Cabinet Name: | First Anders Fogh Rasmussen |
| Cabinet Number: | 70th |
| Jurisdiction: | Denmark |
| Flag: | Flag of Denmark (state).svg |
| Flag Border: | true |
| Government Head: | Anders Fogh Rasmussen |
| State Head: | Margrethe II of Denmark |
| Members Number: | 20 |
| Former Members Number: | 4 |
| Total Number: | 24 |
| Political Party: | Venstre Conservative People's Party |
| Legislature Status: | Minority coalition |
| Election: | 2001 |
| Last Election: | 2005 |
| Legislature Term: | 2001–2005 |
| Predecessor: | Nyrup Rasmussen IV |
| Successor: | Fogh Rasmussen II |
After the 2001 Danish parliamentary election, Anders Fogh Rasmussen was able form a government coalition of his own Liberal Party Venstre and the Conservative People's Party. It was a minority government with the parliamentary support of the Danish People's Party. The resulting cabinet is called the Cabinet of Anders Fogh Rasmussen I. Apart from the EU Presidency in 2002 during which the enlargement of the European Union was decided, the main issues for the cabinet were the so-called tax freeze, which ended the upward drift in municipal income tax rates, tax cuts, law and order, limiting the number of refugees and immigrants coming to Denmark as well as the war in Afghanistan and Iraq.
In the 2005 Danish parliamentary election, Anders Fogh Rasmussen retained his parliamentary support, and was able to reform his cabinet as the Cabinet of Anders Fogh Rasmussen II, with a few changes from the Cabinet of Anders Fogh Rasmussen I.
On 18 June 2002 Flemming Hansen replaced Bendt Bendtsen as Minister of Nordic Cooperation.
In April 2004 Svend Aage Jensby resigned and was replaced by Søren Gade.
On 2 August 2004 there was a cabinet change:
Some periods in the table below end after 18 February 2005 because the minister also serves in Anders Fogh Rasmussens second cabinet.