An experiment to measure single-spin asymmetries of semi-inclusive production of charged pions in deep-inelastic scattering on a transversely polarized He-3 target was performed at Jefferson Laboratory in the kinematic region of 0.16 < x < 0.35 and 1.4 < Q(2) < 2.7 GeV2. Pretzelosity asymmetries on He-3, which are expressed as the convolution of the h(1T)(perpendicular to) transverse-momentum-dependent distribution functions and the Collins fragmentation functions in the leading order, were measured for the first time. Under the effective polarization approximation, we extracted the corresponding neutron asymmetries from the measured He-3 asymmetries and cross-section ratios between the proton and He-3. Our results show that both pi(+) on He-3 and on neutron pretzelosity asymmetries are consistent with zero within experimental uncertainties.