In this article, we have examined the possible interconnection and phase asynchrony between the periodicities of solar wind parameters (solar wind velocity $V$ , plasma density $N$ , and dynamic pressure $P$ ), and the interplanetary magnetic field (IMF) magnitude $B$ , taking into account the polarity state, toward ( $T$ ) and away ( $A$ ) from the Sun, of the IMF. For this purpose, the daily measurements of $V$ , $N$ , $P$ , and $B $ during the period 1967–2018, thus covering almost five solar cycles, were sorted into two groups according to the IMF sense. Days of mixed IMF polarity or having no data were eliminated from our analysis during the entire period. The monthly averages of $T$ and $A$ polarity groups have been calculated for each parameter. $B_{\mathrm{T}}$ ( $B_{\mathrm{A}}$ ), $V_{\mathrm{T}}$ ( $V_{\mathrm{A}}$ ), $N_{\mathrm{T}}$ ( $N_{\mathrm{A}}$ ), and $P_{\mathrm{T}}$ ( $P_{\mathrm{A}}$ ), refer to the monthly averages of $T$ ( $A$ ) polarity group for $B$ , $V$ , $N$ , and $P$ , respectively. In this study, three techniques were applied, including the running correlation analysis, cross-wavelet transform (XWT) and wavelet coherence (WTC) to the monthly means of each polarity group. Our results reveal that the running correlation coefficient for toward and away groups of each parameter reflect a positive correlation value during most of the entire period. The long-term periodicities within the 8–16 yr band are also detected for all toward and away components of the considered parameters with a significant common power during most of the entire period. Moreover, the WTC reflects an almost in-phase relationship behavior between the toward and away groups of each parameter during this range. On the other hand, within the 4–8 yr, 2–4 yr, and 1–2 yr bands, the toward and away groups of each solar wind parameter show mid-term periodicities at different periods, displaying sometimes significant powers.