This paper deals with new convolution properties and some new inversion formulas for the Laplace transforms which are not available in the extensive literature of Laplace transforms. The derivation of these inverse Laplace transforms involves new integral formulas of exponential form. These integral formulas are provided in the appendix. The inverse Laplace transform formulas are presented in a tabular form so that they can be used to solve many problems in applied mathematics and engineering science. © 2013 © 2013 Taylor & Francis.