Studying the constructing mechanism of micro-blog transmission network help to understand the information spreading process on the micro-blog platform deeply, and then obtain effective strategies and suggestions. As for this issue, a directed and weighted network model was proposed. In the model building process, according to the phenomenon that micro-blogs can be transmitted more than one time, triad formation was introduced. Different directions of links were used to represent the various characteristics of active and famous users. Besides, the dynamic evolution process of the link weight was considered. The theory analysis and simulation experiment results indicate the strength distribution, the degree distribution and the correlation of strength and degree obey power-law distribution, and the power exponents are between 1 and 3. Also, this model is characterized by high clustering coefficient and short average path length. Average clustering coefficient is 0.7, and average length is less than 6. As well, actual data of micro-blog transmission were collected to prove the model's correctness.