Biodegradable polylactic acid (PLA) melt-blown nonwovens are attractive candidates to replace non-degradable polypropylene melt-blown nonwovens. However, it is still an extremely challenging task to prepare PLA melt-blown nonwovens with sufficient mechanical properties for practical application. Herein, we report a simple strategy for the large-scale preparation of biodegradable PLA/poly(3-hydroxybutyrate-co-3-hydroxyvalerate) (PHBV) melt-blown nonwovens with high strength and excellent toughness. In this process, a small amount of PHBV is added to PLA to improve the latter’s crystallization rate and crystallinity. In addition, when the PHBV content increases from 0 to 7.5 wt%, the diameters of the PLA/PHBV melt-blown fibers decrease significantly (with the+ proportion of nanofibers increasing from 7.7% to 42.9%). The resultant PLA/PHBV (5 wt% PHBV) melt-blown nonwovens exhibit the highest mechanical properties. The tensile stress, elongation, and toughness of PLA/PHBV (5 wt% PHBV) melt-blown nonwovens reach 2.5 MPa, 45%, and 1.0 MJ·m–3, respectively. More importantly, PLA/PHBV melt-blown nonwovens can be completely degraded into carbon dioxide and water after 4 months in the soil, making them environmentally friendly. A general tensile-failure model of melt-blown nonwovens is proposed in this study, which may shed light on mechanical performance enhancement for nonwovens.