Mm-sized LiMn1-xFexPO4 single crystals with 0 <= x <= 1 were grown by means of the traveling floating-zone technique at elevated Argon pressure of 30 bar. For the various doping levels, the growth process was optimized with respect to the composition-dependant effective light absorption and transparency of the materials. A convex crystal/melt interface, determined by the angle of incident light, was identified to be particularly crucial for a successful growth. The resulting large single crystalline grains are stoichiometric. Structure refinement shows that lattice parameters as well as the atomic positions and bond lengths linearly depend on the Mn:Fe-ratio. Oriented cuboidal samples with several mm(3) of volume were used for magnetic studies which imply an antiferromagnetic ground state for all compositions. The Neel-temperature changes from T-N = 32.5(5) K in LiMnPO4 to 49.5(5) K in LiFePO4 while the easy magnetic axis in the ordered phase flips from the crystallographic alpha- to the b-axis upon Fe-doping of x < 0.2.