The authors consider the problem of numerical inversion of Laplace transform using its values of the Laplace-image defined on the positive real half-axis of the complex plane. The main distinction of the proposed path associated with the method of forming these values. This path is based on a special case of the direct formula of the Laplace transform, when complex variable degenerates into a real variable. As a result, they continue getting image-function, but these functions have an important feature for numerical problems - they have a real argument. The presence of a continuous-time function allows implementing her sampling more reasonably, for example, taking into account the properties of the differentiating features. One more attractive possibility - generalization sampling, conversion and interpolation algorithms for transfer functions with irrational and transcendental expressions. The paper presents the necessary information about obtaining of real functions images and their usage in problems of the Laplace transform inversion. The method is based on the representation of function originals as a segment of series on the exponential Chebyshev polynomials. An example is given.