Vehicles travelling as platoons can reduce the huge traffic jams on the highway. Platoon members can share vehicle information such as speed and acceleration via vehicular ad hoc networks(VANETs) communication to maintain a constant inter-vehicle and inter-platoon distances. However, connectivity is a fundamental measurement to indicate the linking quality of VANETs. This paper analyzes the access and connectivity probability between the vehicles and the road side units(RSUs) of the multi-way platoon-based VANETs with roadside infrastructure. We denote the connectivity probability as the probability that the vehicles on the highway can access to at least one RSU besides the road within a designated number of hops. Moreover, besides considering the connection on the same road, we study the connection between the vehicles and the RSU via vehicles on the nearby neighbor roads. The analytical results have been validated by simulations and results show that the connectivity probability can be improved when there are platoons in a network. Meanwhile, the connectivity probability is higher in the multi-way vehicle-to-infrastructure(V2I) communication network than that in a one-way V2 I communication network. The results in this paper can help to reduce the jams on the highway and achieve intelligent driving. Then the safety and comfort of the drivers and passengers on the highway can be improved. Moreover, these results can provide forceful theoretical support to the future intelligent transportation system(ITS) design. Vehicles traveling as platoons can reduce the huge traffic jams on the highway. However, connectivity is a fundamental measurement to indicate the connection quality of VANETs. This paper analyzes the access and connectivity probability between the vehicles and the road side units (RSUs) of the multi-way platoon-based VANETs with roadside infrastructure. We denote the connectivity probability as the probability that the vehicles on the highway can access to at least one RSU besides the road within a designated number of hops. The analytical results have been validated by simulations and results show that the connectivity probability can be improved when there are platoons in a network. However, the connectivity probability is higher in the multi-way vehicle-to-infrastructure (V2I) communication network than that in one one-way V2 I communication network. Then the safety and comfort of the drivers and passengers on the highway can be improved. Moreover, these results can provide forceful theoretical support to the future intelligent transportation system (ITS) design.