Holm Olaf Bursum (February 10, 1867 – August 7, 1953) was a politician from the U.S. state of New Mexico, whose activities were instrumental for gaining statehood under the Taft Administration and later served as United States Senator from New Mexico.

He attended the public schools in Iowa before moving to New Mexico Territory in 1881.

Bursum was appointed on March 11, 1921, and subsequently elected on September 20, 1921, as a Republican to the United States Senate to fill the vacancy caused by the resignation of Albert B.

Subsequently, Holm Bursum pursued a newspaper career in Washington, D.C. and in New Mexico until his death in 1953.

Through his sister Ruth Bursum's marriage, he is connected to the Paxton family, a name of equal prominence in New Mexico.