The conformal field theory as a subset of quantum field theory has the conformal symmetry. In two dimensions the conformal fields are representation of virasoro algebra that its generators are the modes of energy-momentum tensor of the theory. The conformal transformations in two dimensions are holomorphic maps, in a way that its generators produce an algebra with infinite-dimension. By use of conformal symmetry, we can determine the form of two and three- point functions. The elements of energy-momentum tensor, which is traceless, are divided into two holomorphic and antiholomorphic parts. In the free boson theory, the central charge is equal to 1. And the derivatives of fields are fields with conformal dimension of 1. In fermionic theory, the central charge is equal to ½ and has the conformal dimension of ½. The solutions of three-dimensional BTZ black hole, has been obtained from the Einstein equation in three dimensions with the negative cosmological constant. This black hole has two internal and external event horizons, which divide the space-time into three different regions. Killing vectors, belong to BTZ metric, have time and angular symmetries. Anti de sitter spaces are also the solutions of Einstein’s equation with negative cosmological constant and one can extract BTZ metric by identifying some of its coordinates .there are two integral constants in BTZ black hole metric that are assumed as its mass and angular momentum. In the case that mass and angular momentum are equal (extremal case) the event horizons are coincided together. We solve the geodesic equations by use of killing vectors, then we extract the motion’s trajectory of time-like, light-like and space –like particles. One can see that massless particles can escape from black hole’s gravitational field. If exists a conformal coupled massless scalar field in background BTZ space, the propagators of this field can be obtained from the equation of motion. Then by identifying coordinates and image method, one can get the two-point functions in BTZ coordinates. By use of action and two-point functions, we calculate the expectation value of energy tensor of static and rotating black holes. For static and rotating black holes the energy tensor on the event horizon has a finite value, but in singular point will diverge. If we perturb the metric such that the field’s formations remain invariant, some symmetries would appear which they are symmetry generators that produce the virasoro algebra. In the other word in the boundary of anti de sitter space which the tensor metric is two-dimensional, a conformal field can be defined. the central charge is equal to c=3l/2G.