The magnetic morphotropic phase boundary (MPB) was first discovered in Laves-phase magnetoelastic system Tb–Dy–Co alloys (PRL 104, 197201 (2010)). However, the composition-dependent and temperature-dependent magnetostrictive behavior for this system, which is crucial to both practical application and the understanding of transitions across the MPB, is still lacking. In this work, the composition-dependence and temperature-dependence of magnetostriction for Tb1−xDyxCo1.95 (x = 0.3~0.8) are presented. In a ferrimagnetic state (as selected 100 K in the present work), the near-MPB compositions x = 0.6 and 0.7, exhibit the largest saturation magnetization MS and the lowest coercive field HC; by contrast, the off-MPB composition x = 0.5, exhibits the largest magnetostriction, the lowest MS, and the largest HC. Besides, a sign change of magnetostriction is observed, which occurs with the magnetic transition across the MPB. Our results suggest the combining effect from the lattice strain induced from structure phase transition, and the influence of the MPB on magnetocrystalline anisotropy. This work may stimulate the research interests on the transition behavior around the MPB and its relationship with physical properties, and also provide guidance in designing high-performance magnetostrictive materials for practical applications.