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The field and temperature magnetoresistance dependences of the Si1− xGe x ( x = 0.05) whiskers at low temperatures were studied in the magnetic field range of 0−14 T with using of the Bitter magnet. The investigated whiskers with diameters 5−15 μm were grown by chemical vapour deposition with a doping concentration in the vicinity to the metal-insulator transition ( Nc ≈ 7.8 ⋅ 1018 cm−3). The linear magnetoresistance effect of the solid solution Si1- xGe x whiskers was found in all range of the magnetic fields due to the surface coherence scattering of charge carriers as a result of conduction in the whisker core-shell structure.