Single-molecule fluorescence experiments allow monitoring of the structural change and dynamics of a single biomolecule in real time using dye molecules attached to the molecule. Often, the molecules are immobilized on the surface to observe a longer molecular dynamics, yet the finite photon budget available from an individual dye molecule before photobleaching sets the limit to the relatively poor signal-to-noise level. To increase the accuracy of these single-molecule experiments, it is necessary to study the cause of noise in the fluorescence signal from the single molecules. To find the origin of this noise, the lifetime of the fluorescent dye molecules labeled on surface-immobilized DNA was measured by using time-correlation single photon counting. The standard deviation of the fluorescence lifetimes obtained from repeated measurements of a single dye molecule with the total photon number N decreased as 1/N, thus following a shot noise of the Poisson statistics. On the other hand, an additional constant noise source, which is independent of the photon number, was observed from the lifetime uncertainties from many molecules and became more dominant after a certain photon number N. This trend was also followed in the uncertainties of the single-molecule FRET signals obtained from single and many molecules. This additional noise is considered to come from the inhomogeneous environment of each DNA immobilized on the surface.