We have designed and synthesized a molecular rod that consists of two weakly coupled electronic pi -systems with mutually shifted energy levels. The asymmetry thus implied manifests itself in a current-voltage characteristic with pronounced dependence on the sign of the bias voltage, which makes the molecule a prototype for a molecular diode. The individual molecules were immobilized by sulfur-gold bonds between both electrodes of a mechanically controlled break junction, and their electronic transport properties have been investigated. The results indeed show diode-like current-voltage characteristics. In contrast to that, control experiments with symmetric molecular rods consisting of two identical pi-systems did not show significant asymmetries in the transport properties. To investigate the underlying transport mechanism, phenomenological arguments are combined with calculations based on density functional theory. The theoretical analysis suggests that the bias dependence of the polarizability of the molecule feeds back into the current leading to an asymmetric shape of the current-voltage characteristics, similar to the phenomena in a semiconductor diode.