We present the emission-line profile models of hydrogen and helium based on the results from axisymmetric magnetohydrodynamics (MHD) simulations of the wind formed near the disc–magnetosphere boundary of classical T Tauri stars (CTTSs). We extend the previous outflow models of ‘the conical-shell wind’ by Romanova et al. to include a well-defined magnetospheric accretion funnel flow which is essential for modelling the optical and near-infrared hydrogen and helium lines of CTTSs. The MHD model with an intermediate mass-accretion rate shows outflows in conical-shell shape with a half opening angle ∼35°. The flow properties such as the maximum outflow speed in the conical-shell wind, maximum inflow speed in the accretion funnel, mass accretion and mass-loss rates are comparable to those found in a typical CTTS. The density, velocity and modified temperature from the MHD simulations are used in a separate radiative transfer model to predict the line profiles and test the consistency of the MHD models with observations. The line profiles are computed with various combinations of X-ray luminosities, temperatures of X-ray-emitting plasma and inclination angles. A rich diversity of line profile morphology is found, and many of the model profiles are very similar to those found in observations. We find that the conical-shell wind may contribute to the emission in some hydrogen lines (e.g. Hα, Hβ, Paβ and Paγ) significantly when the temperature in the wind is relatively high (e.g. ∼104 K); however, the wind contribution decreases rapidly when a lower wind temperature is adopted. The model well reproduces a relatively narrow and low-velocity blueshifted absorption component in He i λ10830, which are often seen in observations.