Given an edge-weighted connected graph G on n vertices and a positive integer , a subgraph of G on k vertices is called a k-subgraph in G. We design combinatorial approximation algorithms for finding a connected k-subgraph in G such that its weighted density is at least a factor of the maximum weighted density among all k-subgraph in G (which are not necessarily connected), where implies an -approximation ratio. We obtain improved -approximation for unit weights. These particularly provide the first non-trivial approximations for the heaviest/densest connected k-subgraph problem on general graphs. We also give -approximation for the problem on general weighted interval graphs.