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MgB2+x (x = -0.3 - 3.3) tapes were fabricated by the in-situ powder-in-tube method with two-stage heat treatment, starting from amorphous B powder and Mg flakes to avoid excessive oxidation. The MgB2 tapes without final heat-treatment have a two-stage transition due to inter-granular decoupling. The two-stage heat treatment brought about an enhancement of core density and a strong inter-granular connectivity. Using this method, we studied characteristics of MgB2 tapes synthesized with non-stoichiometric Mg:B ratios on purpose to introduce effective pinning centers such as non-reacted materials and secondary phases. Jc increased drastically with increasing B composition ratio. The maximum Jc reached 1.7 times 105 A/cm2 at 4.2 K, 1 T for MgB2.8, 3.3 times 103 A/cm2 at 4.2 K, 5 T for MgB3.3 and 1.9 times 105 A /cm2 at 20 K, 0 T for MgB2.6. These values are 3-30 times higher than that for stoichiometric MgB2 tape. Analyses based on the grain boundary pinning theory revealed two factors for improvement of Jc. One is an increase of grain boundary density due to suppression of grain growth in Mg poor condition. The other is an enhancement of elementary pinning force at grain boundaries due to the existence of non-superconducting phases. These results are considered to be very useful for further improvement of Jc - B properties in PIT MgB2 tapes.