The present paper deals with a new modification of Baskakov operators in which the functions exp(μt) and exp(2μt), μ>0 are preserved. Approximation properties of the operators are captured, ie, uniform convergence and rate of convergence of the operators in terms of modulus of continuity, approximation behaviors of the operators exponential weighted spaces, and pointwise convergence of the operators by means of the Voronovskaya theorem. Advantages of the operators for some special functions are presented.