This　paper　proposes　a　parallel　in　time　(also　called　time　parareal)　method　to　solve　Volterra　integral　equations　of　the　second　kind.　The　parallel　in　time　approach　follows　the　spirit　of　the　domain　decomposition　that　consists　of　breaking　the　domain　of　computation　into　subdomains　and　solving　iteratively　the　subproblems　in　a　parallel　way.　To　obtain　a　high　order　of　accuracy,　a　spectral　collocation　accuracy　enhancement　in　subdomains　will　be　employed.　Our　main　contributions　in　this　work　are　twofold:　(i)　A　time　parareal　method　is　designed　for　the　integral　equations,　which　to　our　knowledge　is　the　first　of　its　kind.　The　new　method　is　an　iterative　process　combining　a　coarse　prediction　in　the　whole　domain　with　fine　corrections　in　subdomains　by　using　spectral　approximation,　leading　to　an　algorithm　of　very　high　accuracy.　(ii)　A　rigorous　convergence　analysis　of　the　overall　method　is　provided.　The　numerical　experiment　confirms　that　the　overall　computational　cost　is　considerably　reduced　while　the　desired　spectral　rate　of　convergence　can　be　obtained.