The magnetic field dependence of the low-temperature specific heat (LTSH) and I–V characteristics measurements on RuSr2EuCu2O8 were systematically carried out. It is found that the linear-T term γ decreases with increasing H, in contrast to the predicted result for the clean d-wave superconductivity. This finding suggests that the interaction between quasiparticles and magnons be weakened by magnetic field. In addition, the LTSH data exhibits a remarkably large T2 term for both H = 0 and H ≠ 0. The T2 term might be predominately associated with weak ferromagnetism in the Ru sublattice. Furthermore, the effective flux pinning energy E(H, T) determined from fitting the nonlinear region of the I–V curves follows a power-law dependence on magnetic field with an exponent close to −0.5 at a fixed temperature, indicating that the vortex lines of RuSr2EuCu2O8 is quasi-two-dimensional.