Abstract: This research is intended to know the level of student’s critical thinking skill and the influence of critical thinking skill toward student’s social sensitivity about local wisdom in Banyumas Central Java. The research methodologies used were history learning which was emphasized on critical history learning process about local wisdom in Banyumas, the data collections were the essay test was used to measure the level of student’s critical thinking skill conducted in the end of learning process and questionnaire which was used to collect the data of student’s critical thinking skill level about local wisdom in Banyumas and the data analysis was done through the essay test which was used to collect the data about historical critical thinking skill as the independent variable (X), meanwhile, the questionnaire was used to collect the data of social sensitivity about local wisdom in Banyumas as the dependent variable. The influence of X toward Y was analyzed through product moment correlation to know the influence of the two variables. The first was history learning: 30% of the respondents could achieve very good predicate of critical thinking and the score was 3.50-4.00, 40% of the respondents could achieve good predicate of critical thinking and the score was 2.75-3.49, meanwhile 30% of the respondents was only achieve fair predicate of critical thinking and the score was 2.00-2.74. The second was the influence of X toward Y: the influence of X toward Y₁ showed a positive influence yet insignificant (r_calculate = 0.160<r_table = 5% = 0.444 and 1% = 0.561), the influence of X toward Y₂ showed a positive influence yet insignificant (r_calculate = 0.129<r_table = 5% = 0.444 and 1% = 0.561), the influence of X toward Y₃ showed a very significant influence (r_calculate = 0.571>r_table = 5% = 0.444 and 1% = 0.561) and the influence of X toward Y showed a positive influence yet, very insignificant (r r_calculate = 0.030<r_table = 5% = 0.444 and 1% = 0.561).