The Focusing Optics X-ray Solar Imager (FOXSI) is a NASA sounding rocket mission which will study particle acceleration and coronal heating on the Sun through unprecedented high-resolution imaging in the hard X-ray energy band (5-15 keV). Energy release occurring in the quiet region of the Sun may potentially play an important role in the coronal heating mechanism. With a combination of high-resolution focusing Xray optics and fine-pitch imaging sensors, FOXSI will achieve superior sensitivity; two orders of magnitude better than that of the RHESSI satellite. FOXSI requires the spectral capability down to 5 keV, which requires a development of a new ASIC and detector with a better energy resolution. We plan to use a Doublesided Si Strip Detector (DSSD) with a low-noise front-end ASIC as the FOXSI focal plane detector, which will fulfill the scientific requirements on the spatial resolution, energy resolution, lower threshold energy and time resolution. We have designed and fabricated a DSSD with a thickness of 500 μm and a dimension of 9.6 mmx9.6 mm, containing 128 strips separated by a pitch of 75 μm, which corresponds to 8 arcsec at the focal length of 2 m. The DSSD was successfully operated in a laboratory experiment. Under a temperature of 20 °C and a bias voltage of 250 V, we obtained spectra from both sides of the electrodes. The energy resolution was measured to be 980 eV and 2.4 keV for the pside and n-side at 14 keV gamma-ray, sufficient for the FOXSI mission requirement.