3D mesh parameterization is widely investigated with various parameter domains and applied in many computer graphics applications. As many surface meshes are manifolds of genus zero, mapping these meshes onto a topologically equivalent sphere provides some advantages. We introduce an efficient parameterization method based on barycentric embedding for this spherical domain. This method provides an overlapping solution which emphasizes on eliminating the vertex overlappings to ensure bijectivity. Experimental results indicate that it works faster than existing spherical parameterization methods. And we also provide a robust spherical remeshing algorithm based on spherical mesh subdivision. A local recursive subdivision process is employed to cover all the geometric details from the original mesh. Such subdivision process can be controlled to match the desired level of details (LOD), which will create a group of mesh representations with different resolutions. This multi-resolution remeshing framework could benefit various graphical applications including geometry rendering, mesh simplification/refinement, model morphing and etc.