Spontaneous parametric upconversion (SPUC) and spontaneous parametric downconversion (SPDC) have been observed in the β-barium borate (BBO) crystal, and their mechanisms are experimentally and theoretically investigated. SPUC, tuned from $530\text{to}600\mathrm{nm}$ with a FWHM of about $25\mathrm{nm}$ , can be attributed to the sum frequency between the quantum noise and the fundamental laser pulse in the type II phase matching condition $(e+o\to e)$ . SPDC, tuned from $480\text{to}520\mathrm{nm}$ with a FWHM of about $15\mathrm{nm}$ , can be attributed to the difference frequency between the quantum noise and the fundamental laser pulse in the type I phase matching condition $(e\to o+o)$ .