[en] We find that the analytical solutions to a quantum system with a nonpolynomial oscillator potential related to isotonic oscillator are given by the confluent Heun functions $H_c(\mathrm{\alpha <!--\; ??\; -->},\mathrm{\beta <!--\; ??\; -->},\mathrm{\gamma <!--\; ??\; -->},\mathrm{\delta <!--\; ??\; -->},\mathrm{\eta <!--\; ??\; -->};z)$. The properties of the wave functions, which are strongly relevant for the potential parameters a and g, are illustrated. It is shown that the wave functions are shrunk to the origin for a given a when the potential parameter g increases, while the wave peak of wave functions is concaved to the origin when the negative potential parameter $|g|$ increases. Moreover, the wave peaks of the even wave functions become sharper when the potential parameter $a<1$ decreases, but they become flat when the potential parameter $a>1$ increases. When the minimum value $V_{min}=-<!--\; ???\; -->g/a^2$ tends to zero, this nonpolynomial oscillator reduces to a harmonic oscillator.