Phase-contrast imaging using X-ray sources with high spatial coherence is an emerging tool in biology and material science. Much of this research is being done using large synchrotron facilities or relatively low-flux microfocus X-ray tubes. An alternative high-flux, ultra-short and high-spatial-coherence table-top X-ray source based on betatron motions of electrons in laser wakefield accelerators has the promise to produce high quality images. In previous phase-contrast imaging studies with betatron sources, single-exposure images with a spatial resolution of 6–70 μm were reported by using large-scale laser systems (60–200 TW). Furthermore, images obtained with multiple exposures tended to have a reduced contrast and resolution due to the shot-to-shot fluctuations. In this article, we demonstrate that a highly stable multiple-exposure betatron source, with an effective average source size of 5 μm, photon number and pointing jitters of <5% and spectral fluctuation of <10%, can be obtained by utilizing ionization injection in pure nitrogen plasma using a 30–40 TW laser. Using this source, high quality phase-contrast images of biological specimens with a 5-μm resolution are obtained for the first time. This work shows a way for the application of high resolution phase-contrast imaging with stable betatron sources using modest power, high repetition-rate lasers.