Its seem non specific amplification due to following reason:
(1) Nonspecific amplification due to too much template
(2) Many time I get same result when I amplify insert from plasmid having the insert due to low annealing temp.
(3) Use gradient PCR from annealing temp Tm-5 to Tm+5. many time using annealing temp more then Tm will surprisingly gives good specific amplification.
(4) Check primers for their binding specificity.
You can find a lot literature on PCR troubleshooting.
Non-specific amplification. I think if you increase magnesium concentration and annealing temperature, you can get rid of most of the background. Also, include positive and negative controls.
Non specific amplification. Try to increase anneling temperatures, change magnesium concentration. Try to use more purified DNA without contaminations. Perform in non contaminated area. Decrease number of cycles.
I think that the primer specificity is not that good. But it would be easy to analyze the actual cause if you provide the pcr condition. I think you can use a gradient pcr to standardize the anealing temperature. Also use the primer last tool of ncbi to check the secondary targets of these primers.