A three-dimensional hybrid structured-unstructured Reynolds-averaged Navier-Stokes (RANS) solver has been developed to simulate flows in complex turbomachinery geometries. It is built by coupling an existing structured computational fluid dynamics (CFD) solver with a newly developed unstructured-grid module via a conservative hybrid-grid interfacing algorithm, so that it can get benefits from the both structured and unstructured grids. The unstructured-grid module has been developed with consistent numerical algorithms, data structure, user interface and parallelization to those of the structured one. The numerical features of the hybrid RANS solver are its second-order accurate upwind scheme in space, its SGS implicit formulation of time integration, and its accurate modeling of steady/unsteady boundary conditions for multistage turbomachinery flows. The hybrid-grid interfacing algorithm is essentially an extension of the conservative zonal approach that has been previously applied on the mismatched zonal interface of the structured grids, and it is fully conservative and also second-order accurate. Due to the mismatched grids allowed at the block interface, users would have great flexibility to build the hybrid grids even with different structured and unstructured grid generators. The performance of the hybrid RANS solver is assessed with a variety of validation and application examples, through which the hybrid RANS solver has been demonstrated to be able to cope with the flows in complex turbomachinery geometries and to be promising for the future industrial applications.