Dynamic analyses of vibrational motion in cell membranes provide a lot of information on the complex dynamic motilities of a red blood cell (RBC). Here, we present the correlation properties of membrane fluctuation in discocyte and spherocyte RBCs by using quantitative phase microscopy (QPM). Since QPM can provide nanometer sensitivity in thickness measurement within a millisecond time scale, we were able to observe the membrane flicking of an RBC in nanometer resolution up to the bandwidth of 50 Hz. The correlation properties of the vibrational motion were analyzed with the detrended fluctuation analysis (DFA) method. Fractal scaling exponent α in the DFA method was calculated for the vibrational motion of a cell surface at various surface points for normal discocyte and abnormal spherocyte RBCs. Measured α values for normal RBCs are distributed between 0.7 and 1.0, whereas those for abnormal spherocyte RBCs are within a range from 0.85 to 1.2. We have also verified that the vibrational motion of background fluid outside of a cell has an α value close to 0.5, which is a typical property of an uncorrelated white noise.