In electroencephalography (EEG) measurements, processing of periodic sounds in the ascending auditory pathway generates the frequency-following response (FFR) phase-locked to the fundamental frequency (F0) and its harmonics of a sound. We measured FFRs to the steady-state (vowel) part of syllables /ba/ and /aw/ occurring in binaural rapid streams of speech sounds as frequently repeating standard syllables or as infrequent (p = 0.2) deviant syllables among standard /wa/ syllables. Our aim was to study whether concurrent active phonological processing affects early processing of irrelevant speech sounds reflected by FFRs to these sounds. To this end, during syllable delivery, our healthy adult participants performed tasks involving written letters delivered on a computer screen in a rapid stream. The stream consisted of vowel letters written in red, infrequently occurring consonant letters written in the same color, and infrequently occurring vowel letters written in blue. In the phonological task, the participants were instructed to press a response key to the consonant letters differing phonologically but not in color from the frequently occurring red vowels, whereas in the non-phonological task, they were instructed to respond to the vowel letters written in blue differing only in color from the frequently occurring red vowels. We observed that the phonological task enhanced responses to deviant /ba/ syllables but not responses to deviant /aw/ syllables. This suggests that active phonological task performance may enhance processing of such small changes in irrelevant speech sounds as the 30-ms difference in the initial formant-transition time between the otherwise identical syllables /ba/ and /wa/ used in the present study.