We have investigated the structures and properties of the hydrogen bonded complexes formed between HRnCCH and X (X stand for nitrogen, oxygen, water and ammonia) using MP2 (full) theoretical method at the aug-cc-pVTZ-pp for Rn atom and aug-cc-pVTZ for other atoms. In this study, as for the complexes between HRnCCH and X, three stationary structures are located (one annular and two linear structures) corresponding to the true energy minima on the potential energy surface. In these complexes, the red shift of the H-Rn stretch in the linear structure $C_{XA},$ whereas the blue shift of the H-Rn stretch in the structure linear $C_{XB}$ and the structure circular $C_{XC},$ the biggest red shift is -35.71 $cm^{-1}$ in $C_{NH3A}$ and the biggest blue shift is 76.45 $cm^{-1}$ in $C_{H2OB}.$  In addition, we found a tremendous red shift in $C_{H2OC}$ (-154.7 $cm^{-1}$ in O-H bond) and $C_{NH3A}$ (-96.15 $cm^{-1}$ in C-H bond). The most stable structure is the circular structure between HRnCCH and $H_2O,$ whose interaction energies is -27.4 kJ/mol. The origin of the frequency shift and charge transfer in these complexes has been analyzed by the natural bond orbital analysis and atom in molecule. The natural bond orbital analysis indicates the $C\rightarrow \sigma^*_{H-Rn}$ orbital interaction plays a key role in the stabilization energy. The atom in molecule shows the largest the absolute value of V = 0.0220 a.u and the most negative the value of H = -0.0055 a.u corresponding the most stabilization of the circular structure between HRnCCH and $H_2O.$