In this paper, we investigate 273 type II radio burst events detected by Wind, STEREO spacecraft from January 2010 to March 2018 during the 24th solar cycle. We classify all events as five groups or sub-types according to their starting and ending frequencies, and then analyze the observed characteristics of each group of type II radio bursts and the correlation between the occurrence of solar energetic particle (SEP) events and the associated coronal mass ejection (CME) or type II radio bursts. What we find is as follows. 1) In each group of type II radio burst events, the CME speed ( v), width (WD), mass ( m), and kinetic energy ( E _k) associated with SEP events are generally greater than those with no SEP events, indicating that the generation of SEP events requires a fast and wide energetic CME eruption. 2) Compared with type II radio bursts starting from the DH band, type II radio bursts starting from the metric band have a higher proportion of large SEP events. Multi-band type II radio bursts are more likely to produce SEP events than single-band events, where M-DH-KM type II bursts have the highest proportion of SEP events (73%), and the DH IIs only have the lowest one (19%). 3) In each kind of type II radio bursts, the type IIs with SEP events usually have higher starting frequencies (lower shock forming heights), lower ending frequencies (higher ending heights) and longer durations than those with no SEP events; coronal shock waves that are easy to produce SEP events (especially large SEP events) generally begin to form at a lower height (such as < 3 R _s, R _s: solar radius), and are sustained to a much larger height (such as > 30 R _s). 4) There exists a strong negative correlation between the duration and the ending frequency of type II radio burst ( cc= –0.93). The proportion of SEP events increases with the increase of the duration of type II radio burst, and decreases with the increase of the ending frequency, which largely depends on the CME speed and other properties. The results of this paper further show that the generation of SEP events is greatly related to the sub-types and characteristics of type II radio bursts. The higher the starting frequencies and the lower the ending frequencies of type II radio bursts, such as M-DH-KM type II bursts, of which the CME drives to forming shock waves at a very low height and propagates to a very large height, the longer the duration of the shock, the longer the time it takes to accelerate the particles, and the greater the probability of SEP events (especially large SEP events) is.