To provide a melt-blow conjugate fiber nonwoven fabric enabling self-melting adhesion, being bulky, having nonwoven fabric strength, excellent in stretchability and non-slip performance and capable of developing products in multipurpose use and to provide a conjugate composition using the nonwoven fabric.

A conjugate fiber is prepared by a melt blow method and comprises a thermoplastic elastomer in which over half of fiber surface has ≥50 shore A hardness (A) by ASTM-D 2240 method. At least several percentage of adjacent fibers in the conjugate fiber are partially brought into contact with each other during jetting to positively produce lumps partially and locally unevenly distributed and aggregated, entangled, fused and bonded. Thereby, a partially strongly bonded part is produced in a stretchable nonwoven fabric application and an accumulation surface accumulating the conjugate fiber is made uneven in a non-slip nonwoven fabric application.