From the 15 planetary systems that have been detected in binaries only 3 systems are known with close stellar components, i.e. g Cephei, Gliese 86 and HD41004A. The latter is subject of our study presented here. A planetary companion for HD41004A was announced in July 2003. The giant planet (2.3 mJup) moves in a high eccentric orbit (ep=0.39 ± 0.17) around the K1 Vstar with a mean distance of about 1.31 AU. The secondary, a M4 dwarf, surrounds the primary in about 21 AU. Moreover, observations of this system have shown that the M4 dwarf is accompanied by a brown dwarf of 19 mJup, that moves in a very close orbit with a period of only 1.3 days. For this study we concentrate ourselves on the habitable zone (HZ) of HD41004A which is according to Kasting et al. (1993) between 0.48 and 0.9 AU. In a first step we neglected the brown dwarf and studied numerically by means of (a) the Fast Lyapunov Indicator (FLI), (b) the escape times and (c) the maximum eccentricity the existence of a habitable planet. Therefore, we investigated the stability of the HZ for different eccentricities of (i) the detected planet (0.22 ≤ ep ≤ 0.39) and of (ii) the binary (0.1 ≤ eb ≤ 0.7). Due to the high eccentric motion of the detected planet we can restrict the stable zone in the HZ between 0.48 and 0.70 AU. This region is divided into stable islands (for 0.22 ≤ ep ≤ 0.36) due to resonances and for ep ≥ 0.36 only a small stable zone remains around 0.5 AU which might host a habitable planet -- but this depends also on the eccentricity of the fictitious plane