The structural and superconducting properties of a Bi-based compound, Bi2Rh3Se2, are investigated over a wide pressure range. Bi2Rh3Se2 is a superconductor with a superconducting transition temperature, Tc, of 0.7 K. This compound is in a charge-density-wave (CDW) state below 240 K, which implies the coexistence of superconducting and CDW states at low temperatures. Here, the superconducting properties of Bi2Rh3Se2 are studied from the perspective of the temperature dependence of electrical resistance (R) at high pressures (p's). The pressure dependence of Tc of Bi2Rh3Se2 shows a slow increase in Tc at 0-15.5 GPa, and the Tc slowly decreases with pressure above 15.5 GPa, which is markedly different from that of normal superconductors because the value of Tc should simply decrease owing to the decrease in density of states (DOS) on the Fermi level, N(εF), driven by a simple shrinkage of the lattice under pressure. To ascertain the origin of such a dome-like Tc-p behavior, the crystal structure of Bi2Rh3Se2 was explored over a wide pressure range of 0-20 GPa on the basis of powder X-ray diffraction; no structural phase transitions or simple shrinkage of the lattice was observed. This result implies that the increase in Tc against pressure cannot simply be explained from a structural point of view. In other words, a direct relation between superconductivity and crystal structure was not found. On the other hand, the CDW transition became ambiguous at pressures higher than 3.8 GPa, suggesting that the Tc had been suppressed by the CDW transition in a low pressure range. Thus, the findings suggest that for Bi2Rh3Se2, Tc is enhanced through the suppression of CDW transition, which may be reasonable because the CDW-ordered state restrains the charge fluctuation to weaken the electron-phonon coupling and opens the gap to decrease the density of states on the Fermi level. The obtained dome-like Tc-p behavior indicates the possibility of Bi2Rh3Se2 being an exotic superconductor.