Experimentally synthesized perovskite-type YRh3B with a Pm3¯m type structure was proposed as a topological material (TM) via first-principles calculations and the low-energy k·p effective Hamiltonian, which has a quadratic contact triple point (QCTP) at point Γ and six pairs of open nodal lines (NLs) of the hybrid type. Clear surface states observed in the surface spectrum confirmed the topological states. When spin-orbit coupling was considered, the QCTP at Γ transferred to the quadratic-type Dirac nodal point (NP). Under 1% tetragonal strained lattice constants, YRh3B hosted richer topological states, including a quadratic-type twofold degenerate NP, six pairs of open NLs of the hybrid type, and two closed NLs of type I and hybrid type. Moreover, it was proved that the NLs of YRh3B at its strained lattice constants contain all types of band-crossing points (BCPs) (i.e., type I, type II, and critical type). Such rich types of NP and NL states in one compound make it potentially applicable for multifunctional electronic devices as well as an appropriate platform to study entanglement among topological states.