The emergence of unconventional superconductivity is generally considered to be related with magnetic spin fluctuations. Unveiling the intriguing behaviours of magnetic spin fluctuations in mother compounds with layered transition metal ions may shed light on the search for exotic superconductors. Here, based on the framework of the first-principles calculations, we theoretically propose the LaCoSb2 as a candidate mother compound of cobalt-based superconductors, which is a weak antiferromagnetic layered metal but has an in-plane ferromagnetic order of 0.88 µB on Co sites. Importantly, this theoretical finding is supported by our magnetization measurements on polycrystalline samples of the LaCoSb2 experimentally. These results imply a possible p-wave superconductor hosted in the LaCoSb2, once the emergence of superconductivity locates in the vicinity of the verge of the ferromagnetic order, having potential applications in topological quantum computing in future.Introduction.-The studies on the topological superconductors 1-3 have triggered enormous research interests during the recent years, ascribing to these systems hosted the Majorana quasiparticles 4 , which obey non-Abelian statistics and can be used to encode and manipulate quantum information in a topologically protected manner 5 . In solid state systems, the p-wave superconductors 6 or ν = 5 2 fractional quantum Hall states 7 are considered to exhibit Majorana quasiparticles. The first candidate chiral p-wave superconductor is Sr 2 RuO 4 evidenced by previous NMR measurements 8,9 , which breaks the time-reversal symmetry 10 . However, a recent NMR measurement contradicts the previous finding ascribing to the heat-up effect in Knight shift in the NMR experiments 11,12 .Alternatively, a prominent theoretical study predicts the appearance of Majorana bound states at the interface between a topological insulator and a conventional superconductor 13 . A generic theory without any topological insulator is also proposed that considering the combination of Rashba spin-orbit coupling and Zeeman effect as well as the proximity effect from an s-wave superconductor in a two-dimensional metal will induce an effective p-wave superconductor 14 . Experimentally, the indictions of Majorana bound states have been reported in various systems, including the indium antimonide nanowires in contact with the superconductor 15,16 , at the edges of a chain of iron atoms formed on the surface of superconducting lead 17 , quantum spin liquids 18 , and a quantum anomalous Hall effect/supercondctor hybrid device 19 , as well as iron-based superconductors 20 .In this Letter, we theoretically propose the LaCoSb 2