Blazars and gamma-ray bursts (GRBs) both are strong astrophysical events with relativistic jets which point at a small angle from our line of sight. Many recent works suggested that blazars and GRBs may have the similar jet physics. In this paper, we explore a fundamental plane for GRBs and blazars between the peak luminosity (L-peak) and the peak frequency (nu(peak)) with the sample we collected. We find that there is a fundamental plane with low-energy cutoff (LSP) blazars and GRBs. The fundamental plane which we found also exists even after considering the beaming effect on our sample. Our results suggest that these two kinds of sources may have similar radiation process in the synchrotron radiation and this fundamental plane maybe relates to the type of blazars. This might help us to have a better understanding on the theoretical models of blazars and GRBs and the jet physics.