We report an experimental observation of the macroscopic quantum tunnelling (MQT) in a d-wave high-temperature superconductor (HTSC) Bi2Sr 2CaCu2O8+δ intrinsic Josephson junction (IJJs). It is well known that the current-biased Josephson tunnel junction provides an ideal stage for studying a variety of macroscopic quantum phenomena such as MQT. They have been studied and observed in low-temperature superconductor (LTSC) Josephson junctions since the early 1980s and have been established well by now. On the other hand, in the case of HTSC the d-wave pairing symmetry allows for dissipative quasiparticle excitations within the superconducting energy gap, which is expected to severely interfere with an observation of MQT. Contrary to this naive conception, our experimental results have explained that the effects of the nodal quasiparticles are not strong enough to obscure the observation of the MQT. Furthermore, we found that the MQT in IJJs was observed at approximately 1K, which was ten times higher than that of LTSC Josephson junctions. This higher classical-to-quantum crossover temperature is due to their high plasma frequency. We also discuss the resonant activation of IJJs in the presence of microwave radiation.