The insulating and metallic behavior of the grain-boundary weak links has been studied in thallium rich and the samples with small amount of thallium in the charge reservoir layer of Cu1−xTlxBa2Ca3Cu4O12−δ superconductor thin films. The influence of the nature of grain boundaries on the inter-granular critical current density (Jc) has also been investigated. From the power law dependence of Hac∼(1−Tp/Tc)n, it was observed that n=1 gives a best fit for the Jc of thallium rich samples and n=2 provides a best fit for the Jc of the samples with small amount of thallium. The polycrystalline thin film samples showing the power law dependence of Jc as n=1 make superconductor-insulator-superconductor (SIS) type while the samples with n=2 follow superconductor-normal metal-superconductor (SNS) types of Josephson junctions. The insulating grain boundaries decrease the inter-granular Josephson coupling and hence the transport properties are suppressed.