Quantum state tomography is an important step in quantum information processing. For ensemble systems such as nuclear magnetic resonance (NMR), quantum state tomography implies a characterization of the complete density matrix. For an n-qubit system the size of density matrix and hence the amount of information required for tomography is exponential in W. Since, only single qubit single quantum elements are observable in NMR, exponential number of one dimensional experiments with readout pulses to rotate the unobservable elements into observables, have earlier been used to map the density matrix. Recently a novel method of efficient tomography has been developed, which requires constant experimental time for any number of qubits. In this method, all off diagonal elements of the density matrix are mapped using a two-dimensional Fourier Transform NMR experiment and all diagonal elements using a one dimensional experiment. In this Letter, the novel method of tomography is demonstrated experimentally while implementing Grover's search algorithm on a two-qubit system. (C) 2003 Elsevier Science B.V. All rights reserved.