We present the design of a longitudinally diode-pumped Alexandrite laser in continuous-wave operation and resulting performance data. A laser power of 6.5 W in fundamental mode operation was measured, which is, to the best of our knowledge, the highest laser power in fundamental mode operation yet reported. The laser crystal was pumped by two diode modules emitting at 637 nm. The pump radiation was polarization-combined and spatially symmetrized. The laser operates at an output power of 6.5 W with an optical-to-optical efficiency of 26%, temporally stable output with stability of 8% on ms timescale, a beam quality of M2 = 1.1 in both spatial directions and emission of an output wavelength of 752 nm. Measurements of the thermal dioptric power at pumping intensities up to 9.5 kW/cm2 support the appropriate approach of the design. Based on our results, we estimate the potential and show our concept for future scaling of the output power.