The objective of this study was to investigate the static and fatigue strengths of a G40-800/5260 carbon fiber/bismaleimide composite material, a type of high temperature CFRP, at room temperature (RT) and 150°C and to evaluate the practicality of this material. The stacking sequence of the material is quasi-isotropic, 32 plies [+45/0/-45/90]4s. Static tensile and compressive tests were performed at RT and high temperatures for non-hole (NH) and open-hole (OH) specimens. In addition, the effectiveness of notched strength criteria was discussed on the basis of test results. Fatigue tests yielded the S-N relationships of OH specimens for three kinds of stress ratio R (=minimum stress/maximum stress), R=0.1 (tension), 10 (compression), and -1 (tension-compression) at RT and 150°C. This study laid emphasis on investigating the static and fatigue strengths at 150°C and the role of compression load repetition in tension-compression fatigue. Major findings are as follows. (1) Static NH and OH compressive strengths, OH compression fatigue strength, and OH tension-compression fatigue strength were temperature-dependent and classified as matrix-dominant properties. These fatigue strengths decreased with increasing load cycles. (2) An open hole greatly reduced static tensile and compressive strengths at both RT and 150°C. (3) The ratio of compression strength to tension strength under static or fatigue loading was fairly low for both NH and OH specimens at RT and 150°C, except for the case of NH static strength at RT. (4) The compression stress range mostly controlled fatigue lives in tension-compression fatigue tests at RT and 150°C. (5) The material tested showed no large static and fatigue strength reduction at 150°C except for NH compressive strength; however, it should be used with care when structures have open holes and encounter compression loading, especially at high temperatures.