We revisit the one-dimensional quantum system of a sextic potential added with a centrifugal term, $$V(x)=a\, x^{-2}+b\, x^2+c\,x^4+d\,x^6$$ , where the parameters a, b, c and d are arbitrary. We find that its solutions can be expressed as a Biconfluent Heun function $$H_{B}(\alpha , \beta , \gamma ,\delta ; z)$$ , while the associated energy spectrum is determined by the parameter $$\delta$$ . The semi-exact solutions of wave functions fully consist with the properties of the potential.