It happened on path near the Robert Burns Centre just after 5 pm on Saturday.
The man was seen sitting on a bench near the centre and he indecently exposed himself to a family of five who were passing on the way to the nearby play park.
The man is described as being between 30 and 50 years old, about five foot five tall, of big build, with dark short curly hair. He was wearing a light blue shirt and black dress trousers and was carrying a green coloured violin case.
Constable William Dundas at Dumfries said: “We want to hear from anyone who may have been in the area of the Robert Burns Centre around this time to get in touch if they saw this man, or can tell us who he is.”
Police can be contacted through the 101 number.