A new phosphorous-free rhodium supported on a nitrogen-doped silica was successfully used as a catalyst for the hydroformylation of alkenes. The obtained material and the catalyst were characterized by XRD, XPS, FTIR, SEM, TEM, ICP AES, and low-temperature nitrogen adsorption–desorption measurements. The catalytic performance was studied by the example of the hydroformylation of octene-1 at temperatures of 80–140 °C and a pressure of 5.0 MPa. The catalyst provided a 99% conversion of 1-octene with a 98% yield of aldehydes and showed a good conversion of styrene and cyclohexene. The catalyst can be repeatedly used in ten consecutive cycles, with its activity remaining constant.