In order to further explore the oscillation mechanism of constrained droplets in microgravity and extend the application and management of space fluid, the small-amplitude self-excited oscillation processes of droplets that are pinned on a confined substrate are investigated. The substrate has a 5 mm diameter contact circle, which is implemented through the use of a drop tower and high-speed photography technology. Oscillation is a recovery procedure for droplet configuration in microgravity with the confined effect at the boundary, making the contact line and diameter unchanged throughout the entire process. A self-excited oscillation could be divided into two stages: a morphological change process and a small-amplitude damping attenuation oscillation. The first stage is a morphological change process, where the heights of high and low oscillations rise gradually, which in turn correspond to the variation of gravity. And the deformation rate is inversely proportional to the droplet size. The second stage is the small-amplitude damping attenuation oscillation around the equilibrium position until it reaches the final steady state in microgravity. At this stage, the frequency is nearly constant and the attenuation of amplitude represents an exponential damping, like the free oscillation of isolated viscous droplets. The pinning contact line makes the oscillation waveform deviate from sine curve and in the process there exists a period when the heights keep constant at some positions, such as the highest, lowest and others. Studies confirm the hypothesis that the oscillation occurs with the similar second-order mode of free drop when the height fluctuates, and the third-order mode when the height is immobile. This is in agreement with the spectral analysis. Furthermore, when the liquid volume varies within this experimental system, the pinning constraint with fixed contact area on the confined substrate can generate droplets with various static contact angles and undisturbed radii. The deformation stage and oscillation mode of the droplets remains stable, although the concrete courses differ in some ways. In the case of bigger drops, the phenomenon of height unchanging should be in the middle position and vanishes with time. However, the smaller one shows no signs for this condition, and the waveform remains consistent all around. In the second stage, the amplitude decay damping rate and non-dimensional frequency of small droplet are higher.