Tailoring the thermal conductivity of polymers is central to enlarge their applications in the thermal management of flexible integrated circuits. What's more, in practice their thermal conductivity is sensitive to complex physical processes, such as twisting, bending, stretching, compression and temperature fluctuation. Progress has been made over the past decade by fabricating materials with various nanostructures, such as hydrogen bonding polymers with relatively strong chain-chain coupling and stretched polymers with high orientational order parameter, but a clear relationship between stretching effect and thermal properties of hydrogen bonding polymers remains to be established. Here, through molecular dynamics simulations, we firstly calculated the thermal conductivity of single polyvinyl alcohol (PVA) chain and single polypropylene (PP) chain at various lengths, and it was found that they had similar values of thermal conductivity. However, amorphous PVA bulk could form plenty of hydrogen bonds within it due to hydroxyl, which was different from amorphous PP bulk. Next, we numerically studied the thermal conductivity of amorphous PVA bulk and amorphous PP bulk at various stretching rates and different temperatures, respectively. By comparing their thermal conductivity, the differences of thermal conduction properties between hydrogen bonding and non-hydrogen bonding polymers under stretching effect were revealed. In addition, it was found that there were discrepancies of orientational order parameter between hydrogen bonding and non-hydrogen bonding polymers at the same stretching rates. The amount of hydrogen bonds of amorphous PVA bulk with respect to stretching rate was also observed. Our study provides fundamental insight into the improvement of thermal management in polymers.