The spontaneous polarization of pyroelectric crystal is utilized to X-ray emission in low pressure gas of ~1 Pa, which has a potential as a future in-situ X-ray source with small size, light weight, and low electric power consumption. The pyroelectric X-ray production still has problems as its intensity and reproducibility because the mechanism of electron production is still an open question. We have experimentally and numerically evaluated pyroelectric X-ray generation relevant to electric discharges around the pyroelectric crystal with various sizes of target support and target with/without a needle. Three kinds of electric discharge, between crystal top and metallic target (CT-MT discharge), between crystal top and crystal bottom (CT-CB discharge), and along with crystal surface (CS discharge), were observed. The CT-MT discharge was measured by the 1 cm × 5 cm target support or target with a needle, which induced irregular X-ray increases. X-ray intensity became reproducible, but not so large when the CT-MT discharges were measured. The CTCB and CS discharges were active for the large target plates. These two discharges occur irregularly, resulting low reproducibility. While reduction of crystal potential by the CS discharge was not large, the CT-CB discharge stopped Xray emission. When the CT-CB was not measured, the X-ray intensity became large. Calculation results of electric fields at around the crystal supported the experimental results, which implied that selection of appropriate target support is one of important factors to obtain large and reproducible X-ray intensity by the pyroelectric X-ray generation.