We present TangibleGrid, a novel device that allows blind users to understand and design the layout of a web page with real-time tangible feedback. We conducted semi-structured interviews and a series of co-design sessions with blind users to elicit insights that guided the design of TangibleGrid. Our final prototype contains shape-changing brackets representing the web elements and a baseboard representing the web page canvas. Blind users can design a web page layout through creating and editing web elements by snapping or adjusting tangible brackets on top of the baseboard. The baseboard senses the brackets' type, size, and location, verbalizes the information, and renders the web page on the client browser. Through a formative user study, we found that blind users could understand a web page layout through TangibleGrid. They were also able to design a new web layout from scratch without the help of sighted people.