We present a quantity called Mixed number which is the sum of a scalar and a vector quantity. We have developed a Mixed number Lorentz transformation using Mixed number. Most general Lorentz transformation has some limitations but Mixed number Lorentz transformation is free from those limitations. We have applied Mixed number Lorentz transformation in the following different cases - i) Relativistic aberration ii) Reflection of light by a moving mirror iii) Relativistic Doppler’s effect iv) Transformation of the characteristics of a wave The phenomenon of Relativistic aberration, Reflection of light by a moving mirror, Relativistic Doppler’s effect and Transformation of the characteristics of a wave have been clearly explained by special and most general Lorentz transformation and by Mixed number Lorentz transformation. Using Mixed number Lorentz transformation we have observed that the formulae of relativistic aberration, reflection of light by a moving mirror, relativistic Doppler’s effect and transformation of the characteristics of a wave are simpler than the formulae given by most general Lorentz transformation.