New high-resolution spectra, of the chromospherically active binary system CF Tuc, taken at the Mt. John University Observatory in 2007, were analyzed using two methods: cross-correlation and Fourier--based disentangling. As a result, new radial velocity curves of both components were obtained. The resulting orbital elements of CF Tuc are: $a_{1}{sin}i$=$0.0254pm0.0001$ AU, $a_{2}{sin}i$=$0.0228pm0.0001$ AU, $M_{1}{sin}i$=$0.902pm0.005$ $M_{odot}$, and $M_{2}{sin}i$=$1.008pm0.006$ $M_{odot}$. The cooler component of the system shows H$alpha$ and CaII H & K emissions. Our spectroscopic data and recent $BV$ light curves were solved simultaneously using the Wilson-Devinney code. A dark spot on the surface of the cooler component was assumed to explain large asymmetries observed in the light curves. The following absolute parameters of the components were determined: $M_{1}$=$1.11pm0.01$ $M_{odot}$, $M_{2}$=$1.23pm0.01$ $M_{odot}$, $R_{1}$=$1.63pm0.02$ $R_{odot}$, $R_{2}$=$3.60pm0.02$ $R_{odot}$, $L_{1}$=$3.32pm0.51$ $L_{odot}$ and $L_{2}$=$3.91pm0.84$ $L_{odot}$. The orbital period of the system was studied using the O-C analysis. The O-C diagram could be interpreted in terms of either two abrupt changes or a quasi-sinusoidal form superimposed on a downward parabola. These variations are discussed by reference to the combined effect of mass transfer and mass loss, the Applegate mechanism and also a light-time effect due to the existence of a massive third body (possibly a black hole) in the system. The distance to CF Tuc was calculated to be $89pm6$ pc from the dynamic parallax, neglecting interstellar absorption, in agreement with the Hipparcos value.
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