A method to receive payments at obscured addresses
Your algorithm should be secure since it's basicly the same as the "one-time-address"-algorithm in the CryptoNote protocol, which is described as following:


Alice generates two secret keys $a$ and $b$ and publishes $A = aG$ and $B=bG$.
Bob, who wants to send a coin to Alice generates a random $r$ and publishes $R = rG$ and $P = H(rA)G+B$.
Alice (or any party knowing $a$) can check weather a payment belongs to Alice by checking whether $H(aR)G+B = P$. Note that this does not require $b$, so Alice can let any other party check for payment by sharing $a$ without risking them to spend her coins.
When Alice want's to spend the coin, she calculates $x = H(rA)+b$, which is the private key for $P$ since $P = xG = (H(rA)+b)G=H(rA)G+bG=H(rA)G+B$.


Your scheme is a variation of this algorithm with $a = b$ so that $A = B$. This leads to Bob calculation $P = H(rA)G + A$, a check can be performed with $H(aR)G+A = P$ and the secret key being $x = H(aR)+a$, so you can assume it being as secure as the CryptoNote's algorithm (which is pretty secure AFAIK), however you lose the ability to share a view key to let others search for transaction for Alice.