Influenza is a major global public health problem, with serious outcomes that can result in hospitalization or even death. We investigate the causal relationship between human influenza cases and air pollution, quantified by ambient fine particles <2.5μm in aerodynamic diameter (PM). A modified Granger causality test is proposed to ascertain age group-specific causal relationship between weekly influenza cases and weekly adjusted accumulative PM from 2009 to 2015 in 11 cities and counties in Taiwan. We examine the causal relationship based on posterior probabilities of the log-linear integer-valued GARCH (generalized autoregressive conditional heteroscedastic) model with covariates, which enable us to handle characteristics of influenza data such as integer-value, lagged dependence, and over-dispersion. The resulting posterior probabilities show that the adult age group (25-64) and the elderly group in New Taipei in the north and cities in southwestern part of Taiwan are strongly affected by ambient fine particles. Moreover, the elderly group is clearly affected in all study sites. Globalization and economic growth have resulted in increased ambient air pollution (including PM) and subsequently substantial public health concerns in the West Pacific region. Minimizing exposure to air pollutants is particularly important for the elderly and susceptible individuals with respiratory diseases.