Three-dimensional imaging in biological samples usually suffers from performance degradation caused by optical inhomogeneities. Here we proposed an approach to adaptive optics in fluorescence microscopy where the aberrations are measured by self-interference holographic recording and then corrected by a post-processing optimization procedure. In our approach, only one complex-value hologram is sufficient to measure and then correct the aberrations, which results in fast acquisition speed, lower exposure time, and the ability to image in three-dimensions without the need to scan the sample or any other element in the system. We show proof-of-principle experiments on a tissue phantom containing fluorescence particles. Furthermore, we present three-dimensional reconstructions of actin-labeled MCF7 breast cancer cells, showing improved resolution after the correction of aberrations. Both experiments demonstrate the validity of our method and show the great potential of non-scanning adaptive three-dimensional microscopy in imaging biological samples with improved resolution and signal-to-noise ratio.