RuSb₂, as a sister material of thermoelectric material FeSb₂, has been extensively studied focusing on the comparisons with FeSb₂, however, the properties of RuSb₂ under pressure have not been surveyed thoroughly yet. In this work, we studied the properties of RuSb₂ under pressure and explored the similarities and differences of crystal and electronic structures between the Ru-pnictides partners RuP₂ and RuAs₂. Using the crystal structures search method together with first-principles calculations, we found that this family undergoes a serial of structural phase transitions: (I) For RuSb₂: Pnnm → I4/mcm → I4/mmm; (II) for RuP₂: Pnnm → I4₁/amd → Cmcm; (III) for RuAs₂: Pnnm → P-62m. The newly found five phases are all energetically and dynamically stable at high-pressure and exhibit metallic properties. The four high pressure phases of RuSb2 and RuP2 can be quenched to zero pressure. The superconducting transition temperatures of I4/mcm and I4/mmm phases of RuSb2 and I4₁/amd and Cmcm phase of RuP₂ are predicted to be approximately 7.3 K, 10.9 K, 13.0 K, and 10.1 K at 0 GPa, respectively. In addition, the I4/mcm and I4/mmm phases of RuSb₂ and the I4₁/amd phase of RuP₂ exhibit non-trivial topological properties. Our studies illustrate that pressure is an effective way to tune the structural, electronic, and superconducting behavior of the Ru-pnictides compounds.