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.