Online social networks (OSNs) have become an important source of information for a tremendous range of applications and researches such as search engines, and summarization systems. However, the high usability and accessibility of OSNs have exposed many information quality (IQ) problems which consequently decrease the performance of the OSNs dependent applications. Social spammers are a particular kind of ill-intentioned users who degrade the quality of OSNs information through misusing all possible services provided by OSNs. Social spammers spread many intensive posts/tweets to lure legitimate users to malicious or commercial sites containing malware downloads, phishing, and drug sales. Given the fact that Twitter is not immune towards the social spam problem, different researchers have designed various detection methods which inspect individual tweets or accounts for the existence of spam contents. However, although of the high detection rates of the account-based spam detection methods, these methods are not suitable for filtering tweets in the real-time detection because of the need for information from Twitter’s servers. At tweet spam detection level, many light features have been proposed for real-time filtering; however, the existing classification models separately classify a tweet without considering the state of previous handled tweets associated with a topic. Also, these models periodically require retraining using a ground-truth data to make them up-to-date. Hence, in this paper, we formalize a Hidden Markov Model (HMM) as a time-dependent model for real-time topical spam tweets filtering. More precisely, our method only leverages the available and accessible meta-data in the tweet object to detect spam tweets exiting in a stream of tweets related to a topic (e.g., #Trump), with considering the state of previously handled tweets associated to the same topic. Compared to the classical time-independent classification methods such as Random Forest, the experimental evaluation demonstrates the efficiency of increasing the quality of topics in terms of precision, recall, and F-measure performance metrics.