The Electron Spin Resonance in ferromagnetic beta-p-NPNN (T-c = 0.6 K) has been studied for the spherically shaped samples down to 0.4 K. It is shown that the demagnetization effect is particularly important to understand the results both in paramagnetic and ferromagnetic states. The ESR measurements for the shaped samples down to 1 K reveal the completely different g-value temperature dependence from those for the unshaped samples due to the shape demagnetization effect. The resonance line shapes along a- and c-axes become rapidly asymmetric from 2 K and below, indicating the existence of anisotropic relaxation process in the ferromagnetic state. It is shown that the sharp resonance g-shift exists at the ferromagnetic transition temperature in the magneic field along b. Such a shift had been unidentified in the early studies due to the aspheric sample shape. These results can be ascribed to the anisotropic susceptibility due to the low dimensionality of the system. The magnetic resonance below 1 K can be understood as the ferromagnetic resonance with the b-axis as the easy axis.