We report the specific heat (SH) measurements on single crystals of hole doped FeAs-based superconductor Ba 0.6 K 0.4 Fe 2 As 2 . It is found that the electronic SH coefficient γ e (T ) is not temperature dependent and increases almost linearly with the magnetic field in low temperature region. These point to a fully gapped superconducting state. Surprisingly the sharp SH anomaly ∆C/T | Tc reaches a value of 98 mJ/molK 2 suggesting a very high normal state quasiparticle density of states (γ n ≈ 63mJ/molK 2 ). A detailed analysis reveals that the γ e (T ) cannot be fitted with a single gap of s-wave symmetry due to the presence of a hump in the middle temperature region. However, our data indicate that the dominant part of the superconducting condensate is induced by an s-wave gap with the magnitude of about 6 meV. PACS numbers: 74.20.Rp, 74.25.Bt, 65.40.Ba, 74.70.Dd The discovery of high temperature superconductivity in the FeAs-based system has stimulated enormous interests in the field of condensed matter physics and material sciences [1]. The superconductivity has not only been discovered in the electron doped samples, but also in the hole-doped ones [2,3]. The central issues concerning the superconductivity mechanism are about the symmetry and the magnitude of the superconducting gap. The experimental results obtained so far are, however, highly controversial. The low temperature specific heat (SH) measurements in the F-doped LaFeAsO samples revealed a nonlinear magnetic field dependence of the SH coefficient γ e , which was attributed to the presence of a nodal gap [4]. This was later supported by many other measurements based on µSR [5,6,7], NMR[8, 9, 10], magnetic penetration [11] and point contact Andreev spectrum (PCAS) [12]. On the other hand, the PCAS on the Fdoped SmFeAsO indicated a feature of s-wave gap [13], some measurements [14,15,16,17] also gave support to this conclusion. It is important to note that most of the conclusions drawn for a nodal gap were obtained on the electron doped LnFeAsO samples (abbreviated as FeAs-1111, Ln stands for the rare earth elements) which are characterized by a low charge carrier density and thus low superfluid density [18]. For the FeAs-1111 phase, it is very difficult to grow crystals with large sizes, therefore most of the measurements on the pairing symmetry so far were made on polycrystalline samples. This is much improved in the (Ba, S r) 1−x K x Fe 2 As 2 (denoted as FeAs-122) system since sizable crystals can be achieved [19,20]. Preliminary data by angle resolved photoemission spectroscopy (ARPES) on these crystals show two groups of superconducting gaps (∆ 1 ≈ 12 meV, ∆ 2 ≈ 6 meV) all with s-wave symmetry [21,22,23]. It is known that the surface of this type of single crystals decay or reconstruct very quickly, this may give obstacles to get repeatable data when using the surface sensitive tools. Thus solid conclusions about the gap symmetry and magnitude from bulk measurements are highly desired.Specific heat (SH) is one of the powerful tools to meas...