Judicious　Partition　Problem　is　to　partition　the　vertex　set　of　a　graph　such　that　certain　quantities　are　optimized　simultaneously.　Let　k　be　a　positive　integer　and　G　a　graph　with　m　edges.　It　is　proved　in　this　paper　that　the　vertex　set　of　G　can　be　partitioned　into　k　parts　V1,...,Vk　such　that　e(Vi)≤m/k2　+　k-1/2k2(2m+1/4-1/2)+2/3　for　each　i∈{1,2,...,k}　and　e(V1,　.　.　.　,　Vk)≥k-1/k　m+k-1/2k(2m+1/4-1/2)-(k-2)2/8k,　where　e(Vi)　is　the　number　of　edges　with　both　ends　in　Vi　and　e(V1,...,Vk)=m-σki=1　e(Vi).　This　partially　solves　a　problem　proposed　by　Bolloba＇s　and　Scott,　and,　for　some　values　of　m,　solves　the　problem　affirmatively.　©　2014　Elsevier　B.V.　All　rights　reserved.