In this work, we demonstrate that the introduction of pyrene and alkyne groups into a highly conjugated microporous polymer (LKK-CMP-1) can be achieved via oxidative homocoupling of 1,3,6,8-tetraethynylpyrene (L). The 1,3-diyne-linked conjugated microporous polymer not only has good thermal stability but also has small pore sizes. These small pores within LKK-CMP-1 facilitate the interactions between CO2 and its pore walls, evidenced by the high isosteric heats of adsorption of CO2 and also confirmed by ideal-adsorption-solution-theory (LASI) calculations based on single-component-isotherm data. Therefore, despite moderate CO2 adsorption uptake (9.78 wt %, 273 K, and 1 bar) and isosteric heat of adsorption (35.0 kJ mol(-1)) for CO2, LKK-CMP-1 still exhibits excellent selectivities of CO2/N-2 (44.2) and CO2/CH4 (8.2) at molar ratios of 15:85 and 20:80 respectively. In addition, breakthrough experiments have also shown that LKK-CMP-1 is an effective material for CO2/N-2 and CO2/CH4 separations under flowing conditions.