Covalent functionalization of a zigzag boron nitride nanotube (BNNT) with acetylene has been investigated by density functional theory in terms of energetic, geometric, and electronic properties. It has been found that the most stable functionalized BNNT is the one in which the acetylene is diffused into the tube wall so that two heptagonal and two pentagonal rings are formed, releasing energy of 1.54 eV. In addition, the effect of substituting the hydrogen atoms of C2H2 by different functional groups including –F, –CH2F, –CN, and –OCH3 on the geometric and electronic properties of the BNNT has been investigated. The reaction energies are found to be in the range of −1.03 to −3.13 eV so that their relative magnitude order is as follows: C2F2 > (OCH3)2C2 > C2H2 > (CH2F)2C2 > (CN)2C2, suggesting that the functionalization energy is increased by increasing the electron donating character of the functional groups. Overall, chemical modification of BNNT by the studied groups results in little changes in electronic properties of the tube and may be an effective way for the purification of BNNTs.