Selective laser melting (SLM) was used to produce the Ti-43Al-4Nb-1Mo-0.16 (at.%, TNM) alloys with various Y additions. The mechanism of improved formability by Y addition is firstly studied and revealed. Then, the cracking sensitivity of SLMed Y-modified TNM alloys under different Y contents are systematically investigated. Finally, the cracking behavior and control mechanism are proposed. The results show that the improved formability by adding Y to TNM alloys can be ascribed to the good laser energy absorption and lower melt viscosity. Microcracks are easy to form in the SLMed Y-modified TNM alloys despite the improved formability. The crack density decreases as the laser energy density is increased, which roughly satisfies the polynomial y = 0.02x(2)-0.48x+2.56 (R-2 = 0.97). The crack-free samples can be obtained by the addition of 2, 3 and 4 wt% Y with the laser energy density large than 7.001/mm(2). The formation and control of microcracks mainly depend on the microstructure characteristics and phase constitution under different Y contents. The coarse columnar grains, oxygen segregation at grain boundaries, and dominating brittle B-2 phase at lower Y addition (1 wt%) lead to an obvious decline in ductility (with the average microhardness of similar to 596 Hv), thus to induce cracking. By contrast, the fine equiaxed grains, enhanced oxygen-scavenging effect (formation of Y2O3 particles), and decreased brittle B-2 phase content at higher Y additions (2-4 wt%) significantly improve the ductility (with the average microhardness of 554-568 Hv), thus to prevent cracking. (C) 2020 Elsevier B.V. All rights reserved.