Martin, 17, was killed by neighborhood watchman George Zimmerman last month.
The march went from President's Circle to the student union center and several dozen people participated.
"Personally, I want to ensure that Utah went on the record as being one of the states that understood that injustice in any form is not a good thing." said a participant during a speech at the demonstration.
The demonstration is in advance of a larger planned event for Saturday at the Gallivan Center that begins at 5 p.m. Several hundred people are expected to turn out for the march, which is organized by several local organizations.