We realize narrow-linewidth magneto-optical traps of ${}^{46}$Ti, ${}^{48}$Ti and ${}^{50}$Ti atoms based on a 1040 nm-wavelength transition, cooling atoms to a minimum temperature in one dimension of $T_z=990(20)$ nK and a three-dimensional temperature of $T_{3D}=1.28(7)$ µK. Atoms are pre-cooled in a broad-line magneto-optical trap and then transferred with about 25% efficiency to the narrow-line trap. We operate the narrow-line trap in two stages over 85 ms. First, a single cooling beam, blue-detuned from the narrow-linewidth atomic resonance, optically pumps and traps the atoms on a two-dimensional surface where the Zeeman shift from the applied spherical quadrupole magnetic field brings the light nearly to resonance. Second, four additional beams, counter-propagating along the transverse axes, cool and compress the atoms in all dimensions. The high magnetic moment of the laser cooling state makes the dynamics of the narrow-line titanium trap similar to those of other magnetic atoms. We measure the lifetime of the excited state of the transition to be τ = 8.2(9) µs, indicating a transition linewidth of γ/2π = 20(2) kHz, and also measure isotope shifts on the narrow-line transition. We use Stern-Gerlach separation of the ultracold Ti gas to measure the mJ-distribution in the narrow-line magneto-optical trap, finding over 98% of atoms in the stretched spin state.