Hydrogen adsorption is a popular and flexible method to regulate the physical properties of twodimensional (2D) material like recently synthesized biphenylene networks. In this study, mechanical properties and the thermal conductivity () of the fully hydrogenated biphenylene network (HBPN) under strain were investigated systematically by molecular dynamics (MD) simulation and Wavepacket (WP) Propagation method. It was found that HBPN could sustain an unusual strain as large as 28.8% and 34.5% along the zigzag and armchair directions, respectively, which were much larger than the other 2D buckling structure like silicene (about 19.5% and 17%, respectively). Besides, the  of HBPN exhibited an anomalous response to uniaxial tensile strain. Different from its mother structure like graphene, the  of HBPN had an increasing trend with strain explained here with the phononic density of states (PDOS). The physical mechanism behind this non-trivial thermomechanical behavior of this planar sp 2 hybridized carbon allotrope was related to the following two factors. Firstly, the increase of the number of phonons excited at low frequency region which in general carried more energy and secondly the reduction of the number of higher-frequency phonons thus the weakening of the phonon-surface scattering both helped increase the thermal conductivity under strain. Moreover, the strain induced flattening of the structure was another reason to weaken the coupling between phonons with in-plane and curvature vibrational modes. WP Propagation method within MD was also employed to analyze the propagation of phonons inside the HBPN and group velocities, phonon lifetimes and mean free paths were obtained. Our research can provide essential reference for the application of 2D materials in the field of electronic cooling devices and the modification of thermoelectric energy conversion efficiency of materials.