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Low-temperature specific heat is measured on the overdoped Ba(Fe_{1-x}Co_x)_2As_2 (x = 0.13) single crystal under magnetic fields along three different directions. A clear anisotropy is observed on the field dependent electronic specific heat coefficient {\gamma}(H). The value of {\gamma}(H) is obviously larger with magnetic field along [001] (c-axis) than that within the ab-plane of the crystal lattice, which cannot be attributed to the effect by anisotropy of the upper critical field. Meanwhile, the data show a rather small difference when the direction of the field is rotated from [100] to [110] direction within the ab-plane. Our results suggest that a considerable part of the line nodes is not excited to contribute to the quasiparticle density of states by the field when the field is within the ab-plane. The constraints on the topology of the gap nodes are discussed based on our observations.