Isolated spinning neutron stars, asymmetric with respect to their rotation axis, are expected to be sources of continuous gravitational waves. The most sensitive searches for these sources are based on accurate matched filtering techniques that assume the continuous wave to be phase locked with the pulsar beamed emission. While matched filtering maximizes the search sensitivity, a significant signal-to-noise ratio loss will happen in the case of a mismatch between the assumed and the true signal phase evolution. Narrow-band algorithms allow for a small mismatch in the frequency and spin-down values of the pulsar while coherently integrating the entire dataset. In this paper, we describe a narrow-band search using LIGO O2 data for the continuous wave emission of 33 pulsars. No evidence of a continuous wave signal is found, and upper limits on the gravitational wave amplitude over the analyzed frequency and spin-down ranges are computed for each of the targets. In this search, we surpass the spin-down limit, namely, the maximum rotational energy loss due to gravitational waves emission for some of the pulsars already present in the LIGO O1 narrow-band search, such as J1400-6325, J1813-1246, J1833-1034, J1952+3252, and for new targets such as J0940-5428 and J1747-2809. For J1400-6325, J1833-1034, and J1747-2809, this is the first time the spin-down limit is surpassed.