Handwritten document image segmentation into text-lines is a crucial stage towards unconstrained handwritten document recognition. In the context of Indian subcontinent multiple scripts are used for communication where a system for multi-script handwritten text line segmentation is very much essential. In this paper, we present a robust line segmentation algorithm to handle the multi-script text line segmentation problem. This method is capable to overcome most of the hindrance faced by state-of-the-art methods. We carried out experimentation on our proposed Bangla handwritten document image dataset WBSUBNdb_text and also on a variety of well-known public handwritten datasets namely: CMATERdb, PhDIndic_11, KHATT, HIT-MW, ISI Bengali Writer Identification/Verification dataset, ICDAR 2013 segmentation contest dataset, ICDAR 2013 writer identification contest benchmark dataset, and obtained promising results.